It depends on which SRAM shifter. The ones that have a ".0" in the name such as: 9.0sl or X.0 then they are ONLY compatable with SRAM rear derailleurs (although due to the nature of front derailleurs and not being "indexed" like rears you can run a Shimano front; XT, XTR, etc). They are indexed differently than the Shimano stuff. If you find (easily done) SRAM shifters that don't have that designation; example of this would be the "rocket" shifters. Here is SRAM's compatability matrix:
You are asking about using a Shimano shifter with SRAM deraileurs though (I know, I digressed for a minute). It doesn't work all that well to do it the way you asked. I have seen people do it, but they are the ones that ask why their bikes shift mysteriously or don't shift as they should. Good luck.