Mountain bike crank hits derailleur cable
Nope, it won't hurt anything. It's unlikely, but the worst case is that you might knock the cable crimp (the cap on the end of that cable) off eventually, which could then cause the cable to fray, which would then eventually need to be replaced. 

I would try to bend the cable so that it is tucked away behind a piece of the bike frame or the front derailleur (the thing that shifts your front gears) so that it is silent and worry-free.

Enjoy the new bike!