Not if you get a Straight Talk T-Mobile SIM. If you get a T-Mobile AT&T SIM, yes.
If the coverage is the same, make it simple and get a T-Mobile SIM. If T-Mobile doesn't cover the places you need but AT&T does, get the phone unlocked and get an AT&T SIM. (Straight Talk gives you your choice.)
(Since it's not currently active on a T-Mobile plan, you'll have to look on eBay and buy the unlock code. [The IMEI number, which they'll need, is on a label under the battery. It's the one labeled Dec