There will be many ifs and buts here... For one thing, there are no schematics available from raspberrypi.org so we have to assume that the power circuitry is somewhat similar to other models - lets look at the B+. Using the pin header and not the micro-USB port to power the Pi will circumvent the protection circuit including the poly-fuse - you have been warned.
Is the header capable of being supplied 120mA?
It's highly likely that this is possible.
What is the max current that I can supply to the header?
The max amperage of header pins is listed with 1 through 3 A (depending on which product you look). However the Pi Zero does not provide a populated header pin, just via holes in the PCB. So the current is only limited by the width of the traces on the board. I'll go with the educated guess here that the board is designed that way to support the current necessary to operate the Pi.