We have not extensively tested Jolicloud, but on cursory installation tests Crossover seems to work as expected.
Jolicloud 1.0 is an Ubuntu-based distribution, and so we recommend that you use the .deb (Debian) installer package. When you double-click on the .deb installer (or right-click and look for "open with"), Gdebi should open up the package and offer to install it.
After the installation, you'll find that Crossover doesn't readily appear in Jolicloud's menus. To see Crossover's menus, and the launchers for Applications installed in Crossover, push the "menu" key on your PC's keyboard. This is the hotkey in Jolicloud for bringing up the Ubuntu GNOME menu, which will contain Crossover.