More like PayPal will introduce PayCoin, their own brand on top of the Bitcoin system. After they leverage the entire Bitcoin network for free, they will charge both sellers and buyers fees to send PayCoins through it's "secure" network. Since PayPal is already ubiquitous in NA and is required for sites like eBay, everyone will adopt PayCoin and not even know what a "Bitcoin" is. Then they will freeze your PayCoin balance any time you make a transaction they consider "too large". They will reverse payments to sellers because the item "didn't work" or "never arrived" even though you have delivery confirmation. You won't be allowed to use PayCoins to purchase any digital goods either, of course.
Sounds amazing.
Doesnt make any sense for paypal to use bitcoin in the way you describe. They already have their own coin and network. The main difference is their coin is pegged to local currencies, but they can still transfer that money instantly and basically for free from anywhere to anywhere they want. For paypal, bitcoin doesnt add anything in that sense. The only thing paypal can do that does make sense, is accept bitcoins as deposit and convert them to a paypal dollar/euro balance. And perhaps offer a bitcoin wallet service, so you can store bitcoins like you store dollars and euros in your paypal account. Both of those would help rather than hurt bitcoin; regardless if you choose to use it.
I really don't get how Paypal can "integrate" Bitcoin in a way that has a strategic sense for them. Bitcoin is a natural enemy for Paypal, as it's designed to be decentralized (you don't need to trust a third party, so no need to Paypal).