You'll probably need more than just the number.
To open a bank account, you'll need to display ID.
The process is alluded to on the PayPal page that describes verifying
your identity. If you go to https://www.paypal.com/
and open an account, you get the option to verify your identity.
"What does "Verified" mean?
Becoming Verified means that you maintain a confirmed bank account in
your PayPal account. Because banks are required by law to screen
account holders, Verification authenticates a member's identity and
increases the security of the PayPal network for everyone. Verification
not only offers you increased security, it lets others know you are a
confirmed member of the PayPal community."
I don't know what law PayPal is talking about, and I don't know what
"screen" means here either. But my experience is that banks want to see
ID when they open an account, and then they run a Check Systems search
on the SS#.