@Bill E. , correct me if I'm wrong, but doesn't "Rent" come before "Refi", then Repeat?...
Unless this is commercial (and it sounds like you're talking about a SFR) it depends on which appraisal you're talking about. Whether it's rented or not won't impact the appraisal on a SFR because it's done on a comp sale basis, not an income basis. So, the appraisal will be the same whether you have your tenant or not.
If you're appraising for the initial purchase, and you're planning to do a full rehab, however, you'll want to factor in the tenant to your cash flow and timeline after that initial purchase stage. You may not be able to get the tenant out, and do a robust rehab, immediately - which could negatively impact your outlook.
More details on the deal and your timeline would be very helpful in answering your question.