It wouldn't make sense for them to do that, since they are paid for accepted shops. If they were to pre-pay, and your report was rejected, they'd be out that money.
You can sign up for a rewards credit card for that hotel group, pay with the card, and then pay it off in full when you receive reimbursement. That way you rack up extra points, with no real OOP.
I only do hotel shops when I am traveling anyway, so that I get reimbursed twice.
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Plan the work. Work the plan.