It's not something that the current system can handle, so no.
That said, there's some big mystery update coming to the awards system that I'm keeping an eye on, hopefully it adds more features.
Disclaimer for any who are not generally aware: The site awards are a plugin on the community software. Honestly I don't do a whole lot of coding on the site, mostly moving stuff around and implementing plugins. I went with this specific forum software to make it so that if I ever decide to dip out, the community isn't fucked cuz I was the only one who knew how it worked. As it stands I'm the expert with regard to how the site works, and I do most of the work on it, but I'm not Dain - even if I leave the staff will still be equipped to improve the site as they see fit.
This DOES mean that our hands are sooooomewhat tied on a few things, but honestly I think you'll find it's mostly little things like this specific site awards thing where it's more a nice to have, rather than like "God I wish the site was actually secure".