CB and subsequently GJ only support Joomla SEF. Anything beyond this we've no guarantee. In other words it's untested, you can install, migrate from GJ 1.8, test, and if not satisfactory uninstall 2.1 (latest just released).

drdehart wrote: Does this mean that turning on Joomla's SEF function should have some effect on the GJ urls? Because when we do it nothing changes.

Yes, but assuming you created your GJ URLs using the "Create Menu" links from GJs backend (plugin page, category edit, and group edit). The entire link won't SEF as some items are parameters that Joomlas .htaccess does not know how to handle and thus left untouched.

drdehart wrote: what is the alternative for setting up the urls so that Joomla sef will work?

There is no alternative, if you didn't create the links via "Create Menu" then they are not seen as Internal menu links by Joomla and if that's the case then Joomla removes the Itemid. If you want all parameters of the URL SEF then you need to make additions to .htaccess for rewriting their display, but this could cause parts of GJ to fail to function; is untested. Only default SEF rules are tested.