Pre-reg to me, is a description for a vehicle up to a few months old, that has been registered for whatever reason, and has minimal amount of miles. So it should still have most of its warranty remaining, not just some. Arguably pre-reg could also be described as used, but if it only has some warranty remaining, it definitely sounds 2nd hand rather than pre-reg!.

As to the question, no, putting a private reg on it will have no effect on the warranty.