I can share some information regarding running payroll with insufficient funds via QuickBooks Online.
To be in-line with your question, yes, QuickBooks will pay your employees on your behalf if you don't have enough balance to run payroll. However, this will have a balance due on our account since Intuit covers the funds for you.
Your account will remain on hold and can't process payroll unless Intuit receives the payment. You can get more details in this article about NSF Holds: All Online Payroll - NSF Holds.
The following articles are good references as well: