Yes - IF the left hand shifter has enough cable pull to pull the rear mech through all of the cassette width. It is really only designed for the front mech.
Alternatively try downtube shifters on Jagwire bar end mounts:
They are gorgeous to behold, use ti parts and are very light. Downtube or barcon shifters fit straight on giving you loads of choice.
They can be expensive though, I was lucky and found my set cheap via ebay.
*Edit - you will need the round piece shown in the pic - these are specific to Shimano barcons/ bar end shifters and are also used with other handlebar mounted downtube lever adaptors etc...