The answer is absolutely NO, because SMTP and POP are not same but two different servers which are involved in the sending and receiving of e-mails respectively.
To explain this problem,
Let us take an example of 2 systems or pcs which are connected to TCP/IP network, and they communicate through SMTP and POP servers.
Observe! when a pc X sends an e-mail to system Y using server SMTP,
The respective mail is not received to system Y by the same server(which is SMTP),
But! the mail is received through a different server which is POP server.
Above example shows that, there is no involvement of the same server in sending and receiving of a message through TCP/IP network.
Same pattern will be used by all the communicating systems, no doubt a system may be sending message through SMTP at one time, May be getting a message of another system through POP server.