They definitely look and they schedule accordingly for the TBAs. Only admin can see who and how many responded to TBAs, I know a couple of schedulers who use this and they almost always select the most qualified (in there eyes) for the games. Usually loyalty, availability and a good reputation in rinks helps officials to get games. It may not seem like it but if a coach, players, or parents see an official come onto the ice and the collective reaction is "oh no, not him". It is quite likely that the schedulers know this as well. It is not that difficult to have a good reputation as an official, ask some of the more advanced guys for tips or as your scheduler.