All PayPal does right now is help you get dollars from point A to point B, and in the process they take a cut. They could do the same thing with bitcoin. I don't think it would be competition with bitcoin, it would be promoting it to mutual benefit.
I would be afraid of them providing this service without allowing you to export your data, however, which seems like the kind of thing PayPal might like to do. If your bitcoins were trapped in their system you're always in danger of having your account frozen as has been a problem up to now. Part of the purpose of bitcoin is to be able to avoid that, so I'd hate for PayPal to bring that whole problem to the bitcoin world.
But if they approach it properly, bitcoin could be a great opportunity for PayPal, instead of a threat.