A short shifter does put more stress on the syncros and shift forks. However the tranny in the 370Z is really beefy, gear wise and shifter fork wise. However it does have a history of syncro problems in the 350Z. Nissan went through 8 variations of the tranny with many updates to the syncros and shift mechanisms before settling on the version that is now in the 370Z. I believe now most of the bugs are worked out of the tranny and its pretty bulletproof.
I don't think a short shifter will hurt the transmission but it will cause more stress on the shift forks and will wear the syncros faster.