Can you PCS with a temporary profile?

Short answer Yes, should you? No. Reason being is your orders state that you should arrive to your gaining unit able to pass a PT test and HT/WT and be deployable.

Yes

The key word is "temporary" and what the injury is. I think those only last 90 days but I could be wrong. If it's a permanent profile, you'll have to ask your personnel/medical office what the specific restrictions are for the "disability". I think it also depends what the injury is. For example, if you have a sprained ankle and a temporary profile from PT, there's no reason why you shouldn't be able to PCS.

Hey I think so at least Air Force. I crossed trained and had a PT Waiver for a service connected knee. It was a PCS, because school was long. I was older too think that helps?

It's not really the right thing, but I've seen it happen.
Especially if you're not undergoing any special treatment plan.
A sprained ankle isnt going to get you out of a PCS, but maybe a temporary profile while undergoing reconstructive surgery on an ankle would at least have it delayed or new orders cut.