Yes it will work AFAIK
PCIE 2.0 slot is compatible with PCIE 3 cards though it will run the 7850 at PCIE 2.0 speeds not that is an non-issue if you're using 1 card
I actually ran my 7850 in an ASUS p5ke-wifi ap while I was waiting for the rest of my stuff to come in and that was an board with a lower end/concurrent chipset with pcie 1.1