The real answer to you question is it completely depends on where you are, and sometime what the weather is doing, and other things that I have no idea about. If you are going to the north side of baker then the short answer is no you will not have cell reception unless you are very lucky. If you are on the south side of baker then the answer is it depends on where you camp and where you are standing, but dont count on it. If you are on the north side of shucksan (unlikely) they cell reception works. If you are on the sulfide glacier then no you wont have reception. If you are doing the fisher chimneys then you should be fine. All of these things are regardless of the service provider you have, but verizon is best. Text messaging usually works in all places except the north side which it wont.
So the answer is if you REALLY need to be in contact while you are gone you will need to take a satellite phone.
I spend a lot of time on these two peaks and I have a few areas that I know the cell phone works better than others, but I only found them by trial and error over the last five years.