Only if you promise to tell us how much your rig weighs afterwards
Well at more than 500 gramm for the GPU cooler it might add a bit to its weight.. yet as with your girlfriend weight is very subjective...
TBH the CPU cooler is so heavy that I would remove it before transporting my case far distances (i.e. on a way to a lan). Yet removing the GPU will be much less hassle than removing the CPU cooler.