Yes, on most DSCR products the lease rent is the number, or more precisely the lower of the executed lease rent and the appraiser's market rent opinion. That is the standard convention and individual lenders vary, so ask yours directly which figure they use and get the answer in writing before you sign a lease you can't change for a year.
Size the trade. The gap is $150 a month. Against a 1.20x coverage requirement that supports roughly $125 a month of additional payment, and at the rates available in this environment each $100 of monthly payment carries somewhere in the range of $13,000 to $16,000 of loan balance depending on term and amortization. So the below-market lease plausibly costs you five figures of capital recovery, against three or four weeks of vacancy at $1,900, call it $1,400 to $1,900 plus whatever the utilities run. The vacancy is the cheaper option on those numbers unless your market rent read is soft, and that's the assumption I'd stress before anything else. If $1,900 is aspirational and $1,750 is what the unit actually rents for, the applicant is telling you the truth about your market and the appraiser's rent schedule will too.
The conventional path behaves differently. Agency cash-out on a one unit typically doesn't require an executed lease and can use a percentage of the appraiser's market rent estimate, which decouples your leasing decision from your loan size. Whether you qualify for that path depends on your own income and credit profile, so it's worth a parallel conversation.
On the occupied appraisal, tenant clutter and pets don't change a condition rating from a competent appraiser, though they do change photos and photos are what an underwriter sees. The real friction is access. You'll need to give notice under your state's landlord tenant rules, and required notice periods differ by state, so a tenant who doesn't cooperate can stall your appraisal by weeks.
