We imported historical Invoices from a recently acquired company, into NetSuite. Since these Invoices are historical, they are already paid, but their Status doesn't reflect that they're paid because there are no Payments in the system. We want to mark them Paid without having to create Payments for all of them. Is that possible, and if possible, does it cause problems to do it that way?

i don't think this is possible as far as i know. you should have imported that through JE.