For one, I don't think the adhesive is going to stick to the Arctic silver. Your fan may fall off, and short-out your motherboard. Usually people remove the pad (rubbing alchol cleans the residue up nicely) and apply super glue to just the corners of the chip, with the Arctic silver covering up those areas without super glue. Then attach the heatsink.
I guess if you have retaing pins out side of the chip, then yes you could attach it with both, but the idea is to get rid of heat, and that would only create another barrier for the heat to have to dissiptate thru on its way to the heatsink.