@LAI While you can use the Customer Directory for your donor data base, you'll need to add the customers directly either via entering at the point of sale or from your Square Dashboard.
The best solution for registrations with Square would be to charge their registration fee either in person or within a Square Online Store, and be sure to add their customer profile to the sale.
If you're only looking for a way to take down donor info, there might be other solutions that fit a bit better as @RHatch mentioned.
