Can an unlocked GSM that was used on AT&T work for Verizon's

So, today I was looking into buying a used phone from somebody. I get U.S Cellular and Verizon coverage and my area, but AT&T and other GSM carriers are basically obsolete. The phone I was looking at was unlocked, BUT he used it for AT&T and StraightTalk. I understand that AT&T uses GSM technology, which means the use of a SIM card. CDMA means you're digitality tethered to your provider until they unlock it, wherein with GSM, you can basically move between any GSM network provider by changing SIM cards.

However, if I'm correct, Verizon uses GSM technology for their LTE network. So technically, shouldn't the phone work in my area? I would appreciate some enlightenment in this area because I'm confused.

NOTE: the phone I looked at is an 4G LTE phone and I'm asking about this with the intent of using TracFone's Bring Your Own Phone program. I have an iPhone 4s with TracFone's BYOP right now.