No C required, you can just connect to the UI through a socket and often skip the FFI completely. This is my preferred way to use Tk and I don't even consider anything else unless there is a reason. Working this way also has the nice side effect of making the application UI agnostic.
Or is there a way to run Tk as a daemon?
It interfaces to its own internal Tcl interpreter that runs Tk. You can even feed it arbitrary non-Tk commands to eval.
This is a legacy of the trouble Perl/Tk had splitting it out as an independent library which the Tcl devs didn't want to support.