Absolutely. I happen to use Openbox quite a bit myself, it's a very nice window manager.
For the menus, you can use a simple program called obmenu. Openbox stores all of the information for its root menu in XML format, under ~/.config/openbox/menu.xml, if I recall correctly. You can either edit this XML file by hand with any text editor (if you're that crazy ), or you can use the previously mentioned obmenu to do it a little less painfully. Unfortunately, Openbox doesn't come with obmenu (or another really handy Openbox application called obconfig), but both can be installed from a terminal by typing sudo apt-get install obmenu obconfig. Then, you can run them within Openbox to adjust your menus and some common Openbox settings.
So, assuming that you installed Ubuntu with the default GNOME desktop, getting wireless connectivity is also pretty simple. Each time the Openbox window manager is started, it runs an autostart shell script which can contain any shell commands you would like. The file you need is ~/.config/openbox/autostart.sh. If it doesn't exist, you can create the file and then mark it as executable. In the file, all you need is this:
This will tell the autostart script to wait two seconds, then load the Network Manager applet in the background, which comes by default with the Ubuntu GNOME desktop and provides your internet connectivity.
(sleep 2s && nm-applet) &
You might also want to install some other nice programs for use with Openbox that provide a system tray or panel. If you'd like, you can feel free to PM me and I can tell you how I have things set up for myself.
Good luck, and I hope this was helpful!