In that case yes you will probably have a narrow looking chin, although I don't know how true it is that SARPE widens the midface.
I mean they are cutting a piece of the chin for the SG, not the entire chinbone. The piece that they cut off and then bring lower and forward is a more narrow part than your entire chinbone. It's actually kind of ideal for women, but indeed men look better with broad chins.
I had the same issue after my SG(vertical and forward) but decided not to for a widening genioplasty later. It's a lot of work on that area, your chin is gonna get disintegrated lol. What does your surgeon say about it?