I don't think there'd be too much of an audience as there's a kind of nostalgic charm attached to MI1 and MI2; that is, it's the nostalgia that allows one to be completely unaffected by the relatively ancient-looking visuals. I don't think a new game, especially one produced by fans, could really hit the right notes.
A number of fan games were actually released many years ago with the old style (and indeed, some of the sprites were simply taken); unfortunately LucasArts' legal department was in full swing at the time and shut them all down, forcing them to use names and universes unrelated to MI (although the sprites were clearly still stolen in places). They're not remembered too fondly, really.
That said, I don't believe in fan games at all personally and to this day I've never, ever seen one I could truly say is "pretty damn good". The problem is usually derived from fans simply not having the writing ability to come up with dialogue and humour that's anywhere near as funny as the real thing, instead either re-using jokes from the game (turning them into poor running gags) or just using outright stinky humour.