Can I get a list of unprinted checks (unpaid invoices)?

Yes. You may view a list of checks waiting to be printed (sometimes called accounts payable aging) on the Batch Print Payable Checks screen. To print this list use one of the pre-built Data Viewer reports as follows:
Go to Reports > Data Viewer > Expenses and Ledger > Vendor Information Check Summary

Click the Browse Library button at the bottom

Select the desired pre-built report, without voids (first) or with voids (second) and click Install. (You may intall both and choose either one when running the report).

After installation, select the Data View you want to run. Be sure the Parameters Start and End dates include the posting dates of the unprinted checks, then click the Create button.