Maybe... but PayPal is a more well known mode of transaction than bitcoin, and PayPal is accepted on banks, some banks don't accept funds from people who's money came from cryptocurrency... let's just hope that bitcoin would beat PayPal someday
Sadly, that's the harsh reality of Bitcoin and other cryptocurrencies. Since they lack that level of "trust", centralized payment processors like PayPal still have the lead among businesses and corporations alike. But, someday, Bitcoin will reach the level of Visa and PayPal, once it becomes truly scalable. The moment that businesses, merchants, companies, and individuals see faster transactions and cheap payments, they'll quickly switch to decentralized cryptocurrencies due to the benefits that they'll provide over centralized solutions.
Perhaps, PayPal would still exist in the future alongside Bitcoin since it works with fiat currency unlike the latter. But, seeing that cryptocurrencies have increased in adoption and popularity recently, the possibilities of Bitcoin overcoming PayPal, becomes higher each day. Only time will tell what lies ahead for the future of these payment systems. The one that gathers the most number of users, would be the most likely to succeed in the future. Just my thoughts