If I processed payroll on Thursday morning for 1 paper check, when will it arrive? And will it come to the business for dispersement or go directly to the employee?

Thanks for dropping by in QuickBooks Community, @userronnie.

Once you process your payroll using a paper check, there will be no specific timeline on when your employees will receive it. This will only depend on when the employer gives it to their employees. 

In case you will be using the Direct Deposit feature in the future, you can check out its lead time in this article: When do I need to submit payroll to pay employees on time?

This will help you make sure that your employees will receive their pay on time.

I'm just a reply away if you have other questions with the QuickBooks Online Payroll. Just add the details of your concerns in this thread, and I'll help you out.