"Does Turbo Tax support completing Form 1041?"
Yes. In order to prepare Form 1041 for an estate, and the associated K-1(s), you would purchase a copy of TurboTax Business as well as a personal income tax preparation product (see note below).
TurboTax Business: https://turbotax.intuit.com/small-business-taxes/
Note: TurboTax Business must be installed and run in a Windows environment; it is not available as an online product nor will it run natively on a Mac. Further, you still need a TurboTax personal income tax preparation product since TurboTax Business is not capable of preparing individual income tax returns (it can only prepare returns for entities).
