The short, technical answer:
This cannot be done using the primary management tools that come bundled with Microsoft Exchange Server (or Microsoft Outlook, for that matter). The only way that I can think of doing this—and please note that I am very hesitant to suggest this at all—would be to intercept and modify communication between the client and server on the fly (either using a very intrusive proxy server of some kind or through some creative modification of the localization resource dll using the Resource Localization Tool from the Exchange Resource Kit).
That said, before reading any further, please ask yourself "why do I even want to do this, and what are the benefits and/or hindrances for my users, my organization, and me?"
... which leads me to...
The longer, zen mistress answer:
Users are people. People are lazy. If you think that your users will be any less diligent about archiving old email if they happen to know what their maximum quota is, you are deluding yourself. Moreover, users detest having a quota message thrown at them all of a sudden, especially when they didn't even know that they were subject to a quota in the first place. Then, having received the message, the user still has no idea how much they need to archive (because the quota is in megabytes, and mail users tend to think in terms of "number of messages"). So they eventually clean out enough to stop the warning message, and they are back in the position of not knowing when the warning will pop up next. This is just not at all user-friendly, and only serves to exacerbate helpdesk calls from users who are probably receiving the warning at a time when they are hard at work and don't have time at that moment to dedicate to administrative tasks. If the information is easily available (as it is now, the user is empowered by being able to see that they are nearing the need to do some housekeeping and can schedule a time that suits them.
IMHO, the mere thought of taking this long-sought-after informational feature away from your users is a Very Bad Thing™, especially after Microsoft finally made the effort to add it to the software following more than a decade of hearing and seeing their users begging, pleading, kicking, and screaming for a way to see their quota usage.
Please do your users—and yourself—a favor by giving your users the freedom to choose how they want to work. Remember that the less you do to annoy your users, the less they will end up annoying you. Also, the more you empower them now in small ways, the less critical of you and the more willing to try to understand your decisions they will be in the future when you have a justifiable need to impose some kind of restriction on them.
...and one last thing:
Oh, and just in case it was the "pointy-haired boss" that told you to do this and you're just following orders, please sit them down, make them read this, and point out that a complete stranger on the Worldwide Interhighway Superweb took the time to write this answer—complete with a little attention to grammar, punctuation, spelling, formatting, and a sprinkling of tongue-in-cheek humor—so there must surely be some merit to what she is saying, right? ;-)