No.
Unlike the iPhone 4S, the iPhone 4 had two models, a GSM model and a CDMA model.
AT&T uses the GSM standard, and an unlocked AT&T phone will work on any GSM network worldwide, which includes T-Mobile and nearly every carrier worldwide except Sprint, Verizon, and one Japanese carrier.
The iPhone 4S has a dual GSM/CDMA chip in it, so one model works on all networks. However, if you activate it on Sprint or Verizon, you are stuck with that carrier in the USA. Sprint or Verizon will unlock the SIM slot for you to use international GSM carriers though, so you can travel and avoid expensive international roaming charges. AT&T 4S's don't have the CDMA side active, so an unlocked version still won't work with Verizon, though, like the iPhone 4, will work with just about any network worldwide.