Would the AT&T Galaxy S III work on T-Mobile?

Would the AT&T versions of the Galaxy S III and Galaxy Note 2 work on T-Mobile? With HSPA+ and everything? Obviously LTE wouldn't work, but I don't see why they wouldn't work for 3G HSPA+, and on all parts of T-Mo's network, not just the couple of cities that have been converted to support 1900MHz. They have the same chipsets as the T-Mobile versions, right?

How about the One X+? There's no T-Mobile version of that, but it uses an S4 which presumably supports all the right bands since a lot of T-Mobile phones use S4's.

Apologies if this is a stupid question.