If someone really wants to know who's joining, just use the manual option. You can't tell me it's that difficult clicking "Accept" over a name or two a day. At this point most people have joined the big teams, and there will be no new ones until the old ones die, so chances are you'll be clicking accept about twice a month. There's really no need for your log when you factor that in.
As for the T&C mod thing. You should have more faith in them than that. They're chosen by us because they won't abuse their powers. In the extremely unlikely event that the powers are abused, other T&C mods/members/smods would quickly pick up on it even without this log. They'd be banned, people re-join, that's the end of it. At this point you're trying to center an entire idea which would require a fair amount of work, around monitoring those who do the monitoring; and already get monitored by the entire site.
So with that, I can safely say a no.
Voted Best Nazi Mod Ever <3