I'm not a doctor.  This is just based on observation and what I've read.  Please consult with your own doctor and do not take anything here as science / gospel.  The disclaimer for this site applies! (as in all posts)

Depends on the age... If younger, it does moreso.  Kids' bones are so maliable... the resulting pressure does in fact transfer to the chin!  I have seen this more evident in these types of treatments:

Schwartz lower expansion  (flatter, more protrusive chin... wider appearing)
Lower arch holding devices.  (I haven't looked at this enough to know... I suspect this has more to do with keeing the molars from floating anteriorly)  I don't like a fixed arch, but one that allows for natural widening.  Not sure if any exist?

Lower arch holding devices, I personally am not really for.... depending.  I do prefer a more natural aesthetic for facial development and that is typically a healthy face where no braces were needed.  When the #3 back teeth are lost... right around age 9.5 +/- .... the teeth replacing those are actually smaller.  So, what happens is you'll see the lower central incisors (4 of them) go toward those spaces a bit... AND you'll see the set of teeth behind that open space advance (or at least appear to).  In comparing the loss of #3 teeth at different times.... (example... if the second tooth was JUST lost... but the first tooth was previously lost... you can see this coming together of sorts more toward the gap for the first tooth lost, where the second tooth lost has that full space initially.  Some like to maintain the length of this lower arch.  However... in comparing the facial effects of both sides (one more closed and one just gone missing), I had a preference for the natural closure look.  How to tell which is best?  Not sure, to be honest.  When the space is closed, it's closed... right?  The aesthetics cannot be contrasted then reversed, right?  I suppose where there's a will there may be a way... but the back teeth do transition forward.  Cannot tell if they're migrating in bone or if there is a counter-clockwise profile rotation.  Will have to try and observe, but it was not a scientific analysis of the facial profiles for each side being looked at.  It was just an analysis done by looking.  I do believe that the lower front teeth may be able to be pushed forward a bit if desired following closure of those spaces.  I supoose there is some benefit to holding the lower arches, since people do it.  I do see this typically more with those who prefer a finish where the top teeth and the lower teeth are in more alignment.  Example... some prefer a bigger lid that angles in more.  For those who prefer a more up/down alignment of far back molars (less tilting inward), they do prefer to keep more arch length.  This makes sense as the teeth do grow a tad smaller when crowded.  If they have more space to develop in, they can develop to be a bit bigger... to their full potential.

I know that some do keep the arch length.  This may be useful in situations.  However, like you mentioned... it can give the appearance of a larger chin.  This is because just below the lip is flatter and less convex than naturally left alone.  It may also slightly affect mandibular positioning.  I do believe that arch lengthening can be aesthetic in cases... such as where the parents have a pointy chin to begin.  It may give a better facial balance.  However, there are many factors to consider when making these decisions.  Age, treatment objectives, aesthetics, jaw placement (including ultimate rotation) and the current positioning of the condyles.   Additionally, WIDENING the chin side-to-side more (such as done with Schwartz), tends to widen in a less natural fashion.  Typically, the lower arc, similar to the upper, will fan a bit in the back.  The more naturally shaped arcs will offer a more natural bone-structure aesthetic.  However, this does also depend on age - the extent of early intervention carries a much higher weight in the ultimate treatment than someone undergoing treatment when older.  Children who do have Schwartz expansion on the lower may have a slightly larger looking chin.  It really depends on a number of factors, though, such as how much expansion was performed, the child's age, etc.  Additonally, for expansion of the lower arch... I have seen some nice fixed devices that expand in a fan-shape.  The molars are attached in the back and metal arms connect them to a portion in the front.  This keeps arch length as well as allows for widening.  The one that I've seen is spring loaded and corresponds to RPE treatment in its use.  However, for young children (7/8/9ish), often the mandible, left untreated will follow the maxilla (assuming no crossbites) to an extent when the maxilla is treated alone.  The mandble will sustain some widening (of about a third long-term I've seen in a Pub Med article of Dr. McNamara's).  Initially, it appears to follow more,then relapses some gains.  There's an old PubMed article heralding the long-term arch widening benefits of pairing upper palatal expansion with a lower Schwartz.  As teeth do not want to go into cross-bite... the bottom teeth can be trapped in by a narrow maxilla during growth, just as the top teeth are kept wide by expanded mandibular teeth following treatment.  This lower arch treatment can often account for the wide variation in recommended IMW maxillary gains when seeking multiple consults.  Those who pair with lower-arch expansion (braces, Schwartz or other devices) tend to not expand the lid as far, since those gains are more realized (or locked in) than a treatment that is only up top.  Basically, going to a good orthodontist with a good track record whre you trust their work and they seem to know what their doing can go a long way.  I look for several things when picking an orthodontist, and I know I've already posted an article on that.  :-) Hope that was helpful!

Okay, so now as I think on this more... I do like the concept of holding this space... as I prefer a slight counter-clockwise rotation of the mandible.  This would help to offset some of that tilt backwards.  Basically, though... if you find an othodontist for phase 1, they set up for themselves and their own preferences for phase 2.  So... if you take your child to someone who likes a big lid up top then for phase 2 take them to someone who prefers a more top-down alignment... that can be a little hard since they weren't set up as they'd have like to be.  Alternatively, some may say no treatment is needed in phase 1.  These same people may have better tools and techniques at their disposal for phase 2 than others.  So, these are things to keep in mind.  Additionally, pricing may vary based on the setup in phase 1.  I know there are some who offer discounts for phase 2 treatment following phase 1 with the same orthodontist.  That is nice & helpful.   Also, I know sometimes a proper jaw widening in phase 1 can set a child up to never need phase 2.  As phase 2 typically is more expensive, that can be a good cost savings.  However... most parents do not do phase 1, unless there are serious problems.  They usually just do phase 2, and this can give a very nice aesthetic.  Remember that the most aesthetic option is the most natural or more average.  There is a scientific law of beauty relating to averageness.  Most children get braces when they are teens.  This may very well be the best aesthetic.  When getting multiple consults, most will treat regardless.... but if someone doesn't treat or hesitates to... that may very well mean that it is fine to wait!

Simple answer... moreso depending on age.  Yes.