Sharing directories

While connected to the local computer only:

No, it is not possible.

While connected to the network:

The can see shared files on any computer that has "file and printer sharing enabled" ; and a share has been activated.

This also includes shared printers connected to a local computer on the domain.

Since this machine logon to local machine user, it is running workgroup network level. Ok, here is what you could try :

Let's say you want to share machine S (logon to domain) to machine L (local machine). Go to machine S and use the "users and passwords" under control panel to add user account in machine L. Then user S who login to machine S can access machine L. Or you could try sharing to "everyone" which is the default when you share something.

Simple:

net use G: (or any drive letter you want to assign) \\servername\servershare (C$, D$, or any you've specifically created) /user:administrator

The command will prompt for the password of the *local administrator acount on the machine you want to map the share to, as long as that server can be pinged and has file/print sharing turned on.

Just make duplicate local accounts. In other words, whatever username they're logging onto their local machines with duplicate that logon and password on the non DC file server and assign the appropriate permissions on the share for the local account. For example:
Let's say I logon locally to my machine named "netadmin" as "jsmith" and my password is "password." On the file server create a local account call "jsmith" password "password." Then assign the local account "jsmith" on the file server the required permission to the share.

In terms of networking procedure you're commiting an act of malum by managing local accounts, but it should work. Good luck!