Not if you apply to a specialist unit. I'm pretty sure they don't do Tuesday nights.
As an aside, which country are you in? I believe that there is still an AR unit in Biefefeld, Germany, if that's any use to you.
Norway, I had already spoken to the unit I wanted to join, they didnt care where I lived so long as I could make the weekend.
I remember quite a few TA living in Germany and the Netherlands joining us on exercise rather than travel back in the UK, something must have changed, Im not massively bothered but if they said that at the start, it would have saved a lot of time wasted.
Although I still cant find anything online about having to live in the UK or having to attend Tuesday nights.