Generally speaking, compressionless housing will improve indexed shifting, but will have no benefit for friction shifters, and should never be used for brake lines. Usually it's only really important for brifter/ bar end setups. Sheldon Brown explains in detail

Syncros, being quirky things they are, may benefit a whole lot if you're running in indexed mode. Then again, that short run of housing might make no difference at all. But, the only way to know for sure is to run control tests and post your findings here!