I don't see how push starting a 6MT could cause any damage. You are just turning the flywheel with the clutch instead of the starter. Just make sure the ingnition is in the ON position (tap start twice without clutch depressed).
I kinda push started mine the other day just out of curiousity. With all the stuck throttle stories going around I was wondering how you would shut the car off in that situation. Turns out you must hold the start button for almost 3 seconds to get the engine to shutoff while rolling. Then simply tap the button twice back into the ON position put the car in the appropriate gear for your speed and let the clutch out. Voila, push start with no issues.
Now that being said if you have never done anything like this before DON'T TRY IT ON YOUR Z. There are several things that can go wrong if you are unfamiliar with push starting. If the vehicle is going too fast you can easily over rev the engine and cause damage (not likely pushing by hand). If your engine is not functioning properly the excessive turning over of a cold engine could damage things as well.
For me, If I knew the only problem with my car was a low battery or bad starter I would not hesitate to push start.
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09 370Z - FI TDX CBE/Stillen G3/FI HFC's are next
06 Xterra OR - 3" SL - 33" Pro-Comp MT's - Shrockworks Sliders & Rear Bumper/Tire Carrier - Stillen Cross Drilled Rotors/Pads