Yes.  This fact isn’t very well documented and I’ve seen folks who have sold $100,000+ with Paypal tell you it is impossible.  However, not only is it possible, it is actually exceptionally easy for customers.

Briefly, a prospective customer arrives at the start of the Paypal Express (fancy term for “Paypal hosts the checkout flow”) funnel by either clicking on checkout in your shopping cart or clicking on a buy it now link.  That page is presented differently based on whether the customer currently has a cookie with Paypal or not.  

If the customer is cookied:

They are told to log in to their Paypal account.  Here’s an example (I have used my own site’s shopping cart, so you’ll see my payment email address and the name of my product in both screenshots):

If the customer is not cookied:

They get a split screen.  One half of the screen presents a checkout workflow which they can enter immediately.  The other half presents a sign in/sign up with Paypal dialog.

Why Paypal does things this way:

In a word, because it makes them money.  You have to understand that Paypal’s primary source of revenue is interchange fees.  And their primary expense?  Also interchange fees.  When somebody pays $24.95 for a copy of Bingo Card Creator, Paypal makes $1.02.  And if that person paid through a credit card, Paypal now owes about 70 cents, give or take, to the credit card company.  

If, however, that customer had a Paypal balance and paid through Paypal, completing the transaction is free to them — all they have to do is a database update on their own records.  Ca-ching, tripled their profit!  Or, if the person has no Paypal balance but has linked their checking account to their Paypal account, Paypal can do an ACH debit on the checking account for much, much less than 70 cents.  Again, more profit.  

Then there is also the matter that conversions are much higher when all you need to do is convince people to signin and click “Purchase” rather than filling out a dozen fields in a form.  However, for those folks who are holdouts about getting a Paypal account, requiring them to get one costs conversions and thus costs Paypal money.  This is why they continue to prominently offer the “guest” checkout to people who do not have a Paypal account yet.

What this means for you:

Have no fear — Paypal’s check out experience is optimized to make them money, but as a side effect that means it is also optimized to make you money, by automatically presenting all prospective customers with a purchasing option which is appropriate for them.