In general, the Mormons were patriotic Americans but had had no luck with US justice (including the governor of MO issuing an order for genocide -- to exterminate them). They ready to (essentially) leave the US borders, but did send an emissary to DC to ask for federal assistance in their move from persecution. I think they'd be content in any unclaimed/uncontrolled area, whether claimed (but not controlled) by Mexico or claimed (and thinly controlled) by the US. The main impact of the delayed war might be that the US doesn't call for a Mormon Battalion to head to NM. On the one hand, the pay helped provide badly needed capitol to fund more Mormon pioneers and provided some useful trail experience, but it also took many men away from the Mormon wagon/handcart companies, probably slowing them a bit and adding to their troubles.
So, without the war, the Mormons still wind up in UT. At first it's uncontrolled Mexican territory, but then changes to thinly controlled US territory. The delay might delay when the US first tries to extend control in 1857.