Yes, but probably not something as complete as a browser typically found on a desktop machine.  There are some embedded browsers that can be built and work - we've successfully built an embedded version of Konqueror.

It's a fairly straightforward port - first get and build QT/Embedded, then Konqueror/Embedded.

The biggest problem with browsing on the chumby is that it's a pretty poor experience, and the browsers end up being too large for us to include built-in to the system.