Standardbreds are great horses :)
They will learn to trot properly and canter, but they won't win dressage shows at any higher levels. Not because they can't collect (I wish I had a video of Crow when he gaits real good.. that's as collected as you get on a horse! Lifted back, smooth and just flying.. oh well) but they don't move and look just like a dressage horse is supposed to. And it will take more training to get them there, but it's possible :)
Mine is gaited and I don't trot him at the moment. When he trots tho, he trots well, both under saddle and in the pasture. :)
The thing is to work and build the right movement, most standies will prefer to rush off and hurry (they can be a bit hot and nervous, but in a weird way thety're still willing and obedient..very sensetive..) and you just need them to slow down and think and listen to you and ..try to think about what you want, instead of trying to obey before listening to the instruction :P
You need to ride a lot with your seat rather than the reins or legs.
When we taught Crow to canter, we (my trainer and I) just started riding as if we already cantered, moving our hips into canter position and started to ''bounce'' when he was gaiting. He learnt to put a small canter-beat in the gait and it grew untill it was a nice, clean canter :) A little untraditional way to do it, but it worked since he was gaited and since he had learnt from walk to listen to the seat to know how to walk, what speed and what mode. Now he canters from walk and I've even picked it from standing a few times.
If you start working in walk, teach shoulder ins (it'll build muscle to trot properly and canter) and teach the horse to slow down and collect for your seat, you won't have any real problems riding it in whatever gait you want and get a well balanced, strong and obedient horse. :)
*because I know you want pictures!* :P