Generally speaking, as long as the policy stays in force, there is no problem. Plus, if there is an overloan protection rider that would apply (policy must be in force for a certain number of years and the insured above a certain age), then obtaining a new policy would actually be a detriment to the person's situation.
Technically this is a tax question, so I would contact the advanced sales department of whatever company you're thinking of doing a 1035 exchange to, to see if it would make a difference. Plus, make sure you understand all of the policy's riders - especially if there's an overloan protection rider.