Ask the people on this board with severe T+H that have spent months/years in isolation because of their condition... nope, at best you may "habituate" to it. What do you mean by will the brain "filter" it?
Tinnitus Talk Support Forum
I guess some short of TRT, learning the brain that the T is an unimportant signal.
TRT generally involves some sort of whitenoise/sound enrichment treatment. What you're describing may be similar to the "Back to silence" approach that gets mentioned on this board, which I haven't read much about.