If the switch only has a white and black the answer is no. If it is a 3 way, it has to be the full time powered end, if it is a switch with full time power neutral, then you win . Simply find the powered wire(black) and attach the new wire on to it with an extension tail(to attach to the switch. Then tie all whites and all grounds together. Now the full time power will be routed around the switch to the outlet. The tap will allow for the light to be powered as well.
