I don't think it's possible, but that's a really great idea. Even better would be if you could create subsets of fonts to be displayed in the font menu, rather than every font installed.

There's actually a system-wide facility for this on Mac OS X ("collections"), but it's only accessible in apps that use the system font picker (the Fonts window in Cocoa apps).

Maybe someone from Adobe will read this...!

Alternatively, can I just delete those fonts from the system or will it cause problems? I can't imagine any circumstances under which I would want to use Chalkduster.

Here's something I found useful on this topic. The person who wrote it did some testing of what applications break when certain system fonts are missing, and a lot of them are apparently not really necessary.
http://www.jklstudios.com/misc/osxfonts.html

InD CC allows you to have a selection of favorites at the top of the font menu, and only display those if you like…not that that helps you with CS5:~{

Alternatively, can I just delete those fonts from the system or will it cause problems?

Simply open Font Book and deactivate the unwanted fonts.

I use Font Explorer, not Font Book. But AHA! I just figured out how to deactivate the ones the system doesn't need!

View: System Fonts: Show in Smart Sets.

Then you can deactivate most of them (a few are clearly required, and are greyed out) then go to Hide Smart Sets et voila! Thanks Ralf.

Extensis (maker of Suitcase Fusion) has a "best practices" font guide. I haven't looked at it for a while but I think it discusses which fonts are used by the system and which aren't.

http://www.extensis.com/downloads/font-management-best-practices-guides/

I shut off everything it would let me. The only downside is that now Chrome is displaying in Times Roman rather than whatever sans it had been using.