Assuming it does show up on one of your credit reports as an unpaid collection for some reason, a lot will depend on how flexible your Grad Plus lender is.
Some lenders will allow you to file an appeal with documentation. In that case, you would send the lender a copy of a signed letter from the collection agency/dept and a copy of your bank records showing that the money was paid to them.
If your lender doesn't allow appeals with documentation, you'll have to make sure the relevant credit reporting agency (TransUnion, Equifax, Experian) updates your report to reflect that it has been paid off. That can be a slow going process sometimes, and will often take at least a month or more.
In general, most loan companies are just going to check your credit reports. If it's not on the report(s) they check, they don't care. Not all loan companies check all 3 reports.