Sure! In fact, there are several ways to do it, depending on what you want to test.
Before you test, you should be aware of the following:
Assuming you're signed in with your Administrator account, you will see the ADMIN: Customer Account section on the checkout page. Make sure that the order gets associated with your account (selected by default).
Make sure that whatever address you enter on the checkout page is not the same as your Reply To email setting. NOTE: this also applies to forwards that go to the same place.
If you have a credit card module setup, you can simply place an order with your card and then refund it (or not).
This is a clever little trick to test the checkout process and ensuing emails without any money changing hands. Just temporarily enable the Check / Money Order module and place the order using that method.
NOTES:
Testing with PayPal is tricky because you can't send money to yourself. Perhaps you can have someone else purchase with their account, while you watch the process... and then refund the money (PayPal will keep a very small percent). If you really want to do this yourself, you could sign up for a PayPal Developer account and use their sandbox (there's a setting in the PayPal module to enable Sandbox usage).