Indoor wood track? I don't know about the track specific tires, but I'd be surprised if you couldn't get a full season plus out of road tt tires, and you'd only be giving up single digit watts compared to, say, vittoria pistas.
How wide is the rim on those? Is it old school, intended for 19 or 21 mm tire width?
The other reason to ride a different wheel for training is spoked wheels are supposed to be more comfortable, but I've never ridden ac disc/tri/five spoke to have personal experience.