YouTube does support caption files (specifically the SubViewer/.sub and SubRip/.srt). You can find information about searching for captioned videos and reading captions at
http://www.youtube.com/t/captions_about
More information about the specific caption format is at
http://help.youtube.com/support/youtube/bin/answer.py?answer=100077
P.S. Pat just confirmed that Parity can create the correct caption format for YouTube.