Technically, you should be able to do this. Just be prepared for the possible headaches along the way. Thankfully, there’s plenty of guides here on how to do it but just know what you’re getting into and you’ll be fine.
The only thing I can imagine happening is that your TR key may not work with your copy of XP. Occasionally, Microsoft uses distinct keys for retail, OEM, and corporate copies of Windows XP. So, I’ve seen retail keys not work on corporate copies or OEM keys not working on retail copies.