Yes,It will work.
If it's locked other than T-mobile means,you will need to unlock your mobile to work with T-mobile.For unlocking you can approach your service provider or else try to buy an unlocking service from any one of the online unlocking service provider like Wickedunlock.com Here you can unlock your Motorola Q phone at low cost.Once unlock it,you will be able to use your favor carrier when you need.