Well you can inspect the Makefile once generated or look at the README (though in this case it doesn't mention it). However, looking at the manifest for Storable it lists an XS file. That would be a good indicator that it will require a C compiler. To compile you will require console access to the server.

To build it, simply do the old perl Makefile.PL, make, make install but you will have to change the installation point to be your home directory. I can't provide better instructions than those on this site so I suggest you super search around.