Your analysis of the problem is wrong.
The “queue” does not fill up due to people not checking their mail. By the time a mail hits a user’s mailbox, the damage is already done (i.e. the antivirus, antispam checks, etc.)
It really does not matter whether you have 1 message or 100 messages in your mailbox; any new email coming in will use up a lot of cpu resources for scanning. By the time that scanning is done (and it’s only done when the mail is accepted by the system, not when you go and check it), whether or not it stays in the system is really negligible.
As for checking your mail regularly : an argument might be made that checking the mail account more than is necessary actually burdens the servers more than somebody just checking every 3 weeks would, even if a lot of messages pile up.
The program you are referencing is useful, sure, but all it does is increase the load on mail servers.