Straight Talk is a type of carrier known as an MVNO (mobile virtual network operator), which means that it doesn't run or own a wireless network. Instead, it purchases the right to use towers from AT&T, T-Mobile, Verizon, and Sprint
So in theory NO, you would not need to unlock a T-Mobile phone to use it, as T-Mobile is on the list.
But to be 100% sure I would speak to Straight Talk and confirm they will know for sure.