Depends on what you're trying to do. We accommodate the user working across multiple sites in a few ways, but don't automatically create the user in multiple sites (obviously). Some things to note:
1) Facebook Applications are for one domain only. SourceCoast has many Joomla sites running on it ('this' site, /jfbconnect, /jfbconnect/demo are all different Joomla installs). They all use the same Facebook API/Secret key though since they're all on the same domain.
2) Settings like "Facebook User Only" in JFBConnect are great for automatically creating the user's account.. even if they navigate to a 'new' site and have to login, they may not even really notice they created a new account.. they're just in automatically.
3) "Automatically Map Users by Email" is a great setting if you do have something that will sync the user's across sites. When enabled, if a user clicks Login With Facebook, and there's a Joomla account with that email address, JFBConnect will tie them together automatically, no forms or anything.
The above stuff should help, but obviously, testing, planning, and configuring are all going to be necessary stuff along the way. Should need any help though, we'll be here
Hope that helps,
Alex