Nope! The breech face opening in the slide is different, the extractor wouldn't catch the rim of the 9mm case and the magazine feed lips are different. You would have to get a whole new upper end and mags besides the barrel and recoil spring.
You can drop in a 357 sig barrel though. I picked one up from EFK firedragon through arizona gun runners and have been very happy with its performance. I wold suggest though if you go this route to use a 19 or 20 lb hammer spring. To help allow the slide to breech open far enough.
Changing the hammer spring won't change the slide travel. That's determined by the stop surface on the slide and frame. Also watch for unlock timing discrepancies or you'll blow cases. The .357 Sig has a reduced bore so the pressure curve doesn't drop off as fast as the .40. If the gun unlocks too soon, you'll blow cases.