What do you mean by "supported". I have configured TCC to be OpenSSH's default shell. It works but I have to be very careful. If TCC does anything GUI, the session will hang. TCC is capable of a lot of GUI stuff. Removing it all might be quite a chore.
Actually, correction: "Take Command Console". As for operations which bring up GUI/windowed elements--those would need to be trapped and set to fail/return an error code. [IF the session == SSH vs. Console, NO-OP+Error-Code any operation which would generate a GDI Dialog/Window/etc.]
ATERNATIVE(not too serious--this would be serious work): Re-implement GUI dialogs using NCURSES & TWIN(Textmode WINdow), Manager or similar "text-mode GUI" frameworks. [Over the years there have been at least half a dozen such platforms. Handy on low-bandwidth connections! For PC-centric users, have a look at the old DOS "DESQview" product by Quarterdeck.]