This is possible but we are not going to see it years or maybe 10 years from now. The reason for that is because bitcoin is highly volatile and no one would want to buy or pay for things not on a fixed price. For example if a merchandise cost a dollar then you buy it with bitcoin but then suddenly bitcoin's price dipped so that's okay for the consumer since the price is lower but then for the entrepreneur it is a different story. So because of this they would still use paypal for buying or selling this because now, bitcoin is more of an investment that the pure currency. But once bitcoin stabilize we will see it overtake paypal.
I don't think that the volatility of bitcoin will be a problem in this case. Actually, there's a 50% chance that the bitcoin value will go up and 50% chance that it will go down by the time the seller receives the payment from the buyer. The point here is that, no matter what happens to the value of bitcoin by that time, it is still fair transaction since the probability of losing and the probability of gaining from that are equal (the value goes up, the buyer wins; the price goes down, the seller wins).
Another thing, you can even convert your btc to your local currency before doing the transaction, so there's no problem with that one. It is still a fair game. It is up to the buyer or seller to talk about that.
In my opinion, bitcoin can take over paypal as a payment method. I don't even use paypal since it takes a lot of time to set up an account. And those people who don't have credit card/bank account will be able to do online transactions later with bitcoin, so I think, this will be a great thing to watch out in the coming years.