As far as using it on a CDMA carrier like Verizon, no. Not only is it an issue with network compatibility (the iPhone 2G is GSM only) but carriers like Verizon restrict the phones they accept to an approved IMEI/ESN range due to their legacy as a CDMA carrier. You’re also really going to hate using a 2G phone every day as these are slow by the age of the network they run on. The 2G is a collectible.

The other issue is on the GSM side, the big 2 were phasing out 2G at the time and later blocked new activations— these days the network these use is dead end as it is now decommissioned. Ever since moving to GSM, Verizon is a bit more forgiving about device compatibility but they are still a bit picky in the sense a former AT&T phone may not be accepted on their network. Prepaid (Phone in a box) have worse initial restrictions — they will only work on prepaid for the initial year.

They have loosened the policy and allow factory unlocked iPhones starting with the 7, but you can’t take an AT&T 7 and unlock it for their network, as well as the only time they will unlock it.

To add an additional layer of complexity here they also refuse to fully unlock the 4s despite being possible; it can only ever be used on Verizon in the US. The GSM half can be but the primary bands are locked under the CDMA MSL lock that never gets removed. The 5 is not affected due to the FCC stepping in and telling them no, but the 4s is not something they will unlock. Avoid anything older then the 5 with Verizon.