Yes, it is possible but it is not a very good idea. The official answer, is that since plain C doesn't know what a C++ exception is, you can use exceptions in your gtkmm code as long as there are no C functions in your call stack between the thrower and the catcher. This basically means that you have to catch your exception locally.
Another (the unofficial) answer is that you can recompile glib and Gtk+ (and any other libraries you use) using the -fexceptions flag which will make them exceptions-aware. You can do this as follows:
export CFLAGS='-fexceptions' |
./configure |
make |
make install |
However, the caveat here is that the -fexceptions is a GNU gcc specific flag which is not portable to other compilers. Also, you can't really expect all your users to recompile all their libraries just to use your program. Worse, propogation of those exceptions will break the flow of Gtk+ and thus result in memory leaks. As such, in the current state of gtkmm, exceptions are of limited use. Currently, no reasonable solution has been found for this problem.