No. There's no way to force what you're looking for within JFBConnect. You do not want user's to be able to register on your site, in Joomla, using a username with a space. That's outside of JFBConnect's control altogether and is not related to JFBConnect.
When a user clicks the Login With Facebook button, they're brought to JFBConnect's registration page. Here, we can help you to prevent users that are registering using Facebook to not use a space in their name. For any users that aren't registering through Facebook, they would use the normal Joomla registration process, which we have no control of.
On this site, we let users register through Facebook, which we have set to the User Creation mode of "Facebook User Only", which automatically creates a username for them. If they want to register 'normally', they're brought to Joomla's standard registration where they could choose a username with a space.
There are likely extensions and add-ons for Joomla that can prevent users from creating normal Joomla (non-Facebook) accounts without spaces, but I don't know of any off-hand. We'd recommend you try the following resources to either find such an extension or ask about how to make the changes you're looking for:
Joomla Extension Directory
Joomla Forums