Unfortunately, no. Boost Mobile and T-Mobile are 2 carriers that are not compatible. These carriers are powered by different software technology / network technology.
You will be able to take your phone to another carrier powered by Sprint (Boost Mobile is powered by Sprint).
In terms of taking your Boost phone to another carrier powered by Sprint, the Boost Mobile websites states that it depends on how long you have had your device or how long it has been in service whether or not you are eligible to bring that device to another carrier.
If you have been making payments on your device or if it has been in service for more than 12 months then you are good to go! Boost website that may be beneficial to your question...Eligible customers can request a DSU-capable device be unlocked and/or request the associated MSL Code by contacting Boost Mobile Customer Care at 1-888-BOOST-4U.
With the device being unlocked, you have a lot of available service options that I would consider checking out. I have created a list of carriers compatible with your device that might be beneficial to you! These carriers run off the Sprint network and offer great data plans, low monthly cost.
You can compare all your options here