phone the tac on drill night and arrange to come in and start the application process and see how far down the line you get. I was given at least 4 different answers to a similar question by 4 different people at the local AFCO/ different unit etc etc. I found the best approach is just to start the process. If you dont make the grade first time round, you'll have a better idea of what to expect the second time round.
Look, the medical standards are the same for the TA as the Regular Army, its One Army now. Sorry Steff but its for your own good, a lung full of smoke, CS (or whatever we use these days) is not good for most, let alone someone with a recent history of asthma. Not to mention Ops etc, how would you feel if we had to call a Chinook to pick you up due to an asthma attack ( Hot dusty place!) and some poor sod catches something coming the other way and needs that help too?