Yes! Yorkies can do agility. I actually know one who competes. The height a dog has to jump is based upon their height at the withers/shoulder. In TDAA a dog greater than 4" and less than 8" jumps at 4". In TDAA the equipment is also scaled down for small dogs, which makes it MUCH easier for the dog to do contact obstacles.
You will LOVE trialing your Yorkie in TDAA!
We do both TDAA and AKC (among others).
TDAA is WAY MORE FUN than AKC.
The equipment is scaled down for the smaller dogs and they jump dogs up to 18" so there are some small border collies there.
TDAA is very casual and everyone is very friendly; you don't get the "snobby" attitudes you often find at AKC events.
Most TDAA clubs also serve free snacks and beverages!
You will have more runs and fun games in TDAA whereas AKC will usually only have two runs and you most likely will be there all day waiting for your run (which can get boring for some people).
Often times AKC does not take the "little" dogs too seriously in the sporting events, and I have even heard judges complain that the little dogs are just a waste of time in AKC.
We run small dogs (8" jump height), so it's always kinda hurtful to have to deal with the bigotry against the smaller dogs entered in the AKC sporting events.
You don't have to run out and buy a bunch of expensive equipment to start your training but I would highly recommend joining a club where they offer training since you will definitely need the training. We make all our own jumps out of PVC pipe. We buy used tunnels at the agility events. We don't bother with any large equipment since the clubs have 'em and we just use their equipment during training. We did buy a teeter, though, since that takes a bit more at-home training for faster running contacts.
All-in-all, you'll have a whole lot of FUN!
Your Yorkie will enjoy it, too!