email pop3 question

[David Banning]

I am using dovecot email on my server - Users can connect via IMAP or POP3.

I have a user who is using pop3 but not removing the email from the 
server - so the email stays on the server, -and- it is collecting on their
computer - as the emails build up, will there be a problem with this?

For IMAP it stays on the server, so I assume the server will not be presented
with any problem - but will the user suffer any problem eventually?