You shouldnt have a problem running 1600Mhz ram, if your mobo supports max 1333Mhz, it will downclock itself. You could overclock your memory to get 1600Mhz.
can you please be more specific about which motherboard you have? usually the 1600MHz RAM will downclock to any of these 1333/1066/800 speeds. since 2200MHz is supported, i believe your motherboard can run the 1600MHz RAM at stock speeds.
Motherboard is Gigabyte GA-H61M-S1 and the ram is Kingston HyperX Fury 2x4Gb @ 1600MHz