Absolutely. Companies approach Braintree because they want a no-bullshit payments processor. Based on PayPal's past antics it hardly it hardly has the reputation for which people seek Braintree.
I think this is the perfect opportunity for Stripe, and other payments processors that cater to younger more progressive companies, to get some clients to jump ship.
To read people like Patrick McKenzie, who ran businesses on Paypal and don't have a lot of negative things to say about their underwriting process, two big reasons why they've moved to Stripe:
(1) The Paypal API is apparently extremely complicated
(2) Processing payments with Paypal takes your users off your own site, which costs conversions
Buying Braintree could immediately address both those problems for Paypal.
Yes, PayPal is awful once you've used Stripe and Braintree. I hope that if this happens PayPal just lets Braintree operate as it has before. Legacy PayPal users can keep PayPal, and PayPal doesn't have to fight the battles it has been fighting to keep customers from jumping ship, and can just onboard them to Braintree. Unfortunately, I'm not super optimistic about PayPal's competence.
I think this is the perfect opportunity for Stripe, and other payments processors that cater to younger more progressive companies, to get some clients to jump ship.