It depends on a number of things.
First, do you want it to?
If yes, great, it will, provided it is set up correctly, ie workgroup name in identification.
If you don't, just give it a bogus workgroup name. Of course, this assumes that the user doesn't know the name of the workgroup, or how to correct the bogud name.
If all you want them to be able to do is browse the internet, that's not a problem.
If you want them to use the email service provided by e-smith, you'll have to experiment with that one. I don't see why it wouldn't work.