I don't run VIsta, but I run XP with multiple accounts. I usually create a new account for each Oblivion or Fallout 3 character to keep the files seperate.
And I am able to play Fallout 3 on XP on accounts that don't have administrator privileges. However, I put all my non-admin account into a Windows Group, and then allow access to all files under the Fallout direction to members of that Group. Exactly how to do might be complex to explain here, but you can probably research using Microsoft Help and the Internet.
So unless there is some major step back in Vista on this, I the answer should be no you don't need admin privileges to play Fallout 3, as long as the account has complete control permissions to all files under the Fallout directory.