Assuming the bit fits on the arbor and can be secured, everything should be fine. A 3-wing cutter will give you a slightly better cut than a 2-wing cutter, BTW.
Which depth do you want to adjust? The depth of the slot made by the cutter? Or the position of the slot on your board?
The depth of the slot is adjusted by changing the size of the bearing installed on the arbor. You do have a bearing, don't you? If not, your slot cutter was designed to be used with an edge guide; the edge guide will be used to adjust the depth of the cut in this case.
The position of the slot on your board should be adjusted on the router itself.