Aren't Pagers already obsolete?
The technical answer to your question is this: if a certain pager runs an OS that is capable of running WhatsApp, and if that pager has the hardware requirements for it, then yes. It is also possible that a pager has been configured with an account number tied with his or her WhatsApp account such that messages are forwarded to the pager. But then, what are the chances of that happening? Besides, aren't pagers designed only to receive messages, not to send messages?
It's most likely your friend either wanted to refer to something else but then mistakenly called it a "pager", or he or she is kidding with you.