Assuming there aren't soundness issues with the horse... If the horse is in good health, good physical condition, and has good conformation, then I would think a 15 year old horse could be perfect for a developing dressage rider. You'd have to confirm with the seller, but usually at 15 the horse has show experience, and more of a "been there, done that" type response to training and showing. It's a little easier to work with a good older horse, then buy a youngster that's still reactionary to new things.
An acquaintance of mine recently got back into riding dressage and she purchased a 16 year old TB that had been trained through First Level. The horse has arthritis, but it's manageable with injections. The horse isn't built for dressage really, but he's perfect for the beginner adult ammy.
Another friend of mine has a 15 yr old TB. He had dressage training from 4 -6 years old, but hasn't had any real dressage training for the past 7ish years. Since the horse is older, and had some basic dressage training, they were able to progress pretty quickly to Second level (about a year). They're now working on flying changes for Third level, his half-pass is to die for, and he's got a work ethic I would kill to have in a horse. He's sound, but does start off stiff so you have to take your time warming him up and getting him stretched out properly before beginning work on anything.
My mare's 9. We'll be showing Second next spring. We're training Third currently. She'll be 10 next spring. So she'll probably be 11 by the time we're showing Third level.
15 isn't a bad age (depending on how sound the horse is) for a lower level dressage horse. I think it depends on your goals though. If you're looking to keep advancing through the levels, past Second, then what will you do with this horse once you've outgrown it? It may be a fantastic horse that could take you through Fourth before it's near retirement.. but what if Second is the highest this horse could go? By then, the horse would be 17/18 years old. Do you have the capability to give it a retirement home? What happens if you can't find a good retirement home for the horse when you can no longer ride it?