There's nothing to outright prove he doesn't have a 3rd PayPal account, but I'm not sure what Phil would gain from having it, unless he was trying to commit some kind of financial fraud. Given his current situation and all the examples of Phil being an idiot with finances, it seems incredibly unlikely.
If he's doing behind the scenes transactions, which I do think is a strong possibility, he doesn't need a secret 3rd account. He only wants to hide those because it doesn't support his begging narrative if people see how much money he's actually making. That's why with Tut and the like, he was frantically trying to spin why getting thousands of dollars was actually a bad thing for him and how it meant he actually needed even more money.
The main reason I don't think Phil has a 3rd PayPal account is how lazy he is, even when it comes to financial stuff. He was too lazy/stupid to setup an Amazon wishlist for the longest time, and even when he did and was actively getting stuff, he couldn't keep up with it. Same deal with his Patreon, that's basically free money for him but he barely puts any effort into it. He was also too lazy to rent out his apartment because it would involve having to talk to someone on the phone.
If Phil were doing behind the scenes stuff, which again, I think is a strong possibility, he'd be just as lazy about it as he is with all of his other ventures. He'd just tell them to send it to his standard PayPal so it was one less site he had to login to or setup to automatically have his money withdrawn. I also don't think he's doing that much behind the scenes stuff. Most of his paypigs want the attention associated with sending money, that's why they do it while he's streaming. Even when they do it outside of Twitch, they tend to bring it up in chat, mentioning that they bought a game or controller or whatever from the wishlist. There are some paypigs that I think are afraid of being doxed, Jeff being a prime contender for that. Even if there's one or two other people trying to donate anonymously outside of streams, I can't imagine it would amount to that much money, certainly not enough to justify (in Phil's mind) all the extra effort of setting up a 3rd PayPal account.
The other potential issue is the email might be associated with a PayPal account, but that doesn't mean it is a new account. I just checked on my account, if you add a secondary email address, you can use that email to login to your account. If Phil was trying to consolidate everything under one email after his password leaked, he could have made the new account and linked it to his existing PayPal.