Recently the STEAM registery files have been updated to add a possible game ID for a demo version of L.A. Noire. ClientRegistery blobs are often used to get STEAM clients ready for new games, such as the L.A. Noire demo which is currently listed under ID 202430.

All in all, it's safe to say that a demo version of L.A. Noire for the PC is coming very soon. The game is set to release in just 2 weeks time so there is plenty of time for Rockstar and Valve to roll out a demo version on the STEAM platform.

Thanks to @nikymatev for sending this in!