Yes. You wire up the lights according to the provided diagram, except for where the wires run to the switch. Let's say for example that with the provided relay you have wires heading in three directions. First off is wires heading to the battery, then wires heading to the lights themselves, then wires running to the switch. In some relays this can be only one wire, in others it can be two or three, depending on switches provided. You'll want to cut all b the "hot" wire. This "hot wire" you will want to splice into the hot wire for your high beam, and you should be set! By doing this, the lights are getting allt he power they need from the battery, you aren't overburdening the stock relay, wiring, or switches. The relay only needs a few watts coming from the switch so this method works fine. When you activate the high beams, it sends the signal through its own relay of electricity to the wire heading to the lamps. This signal is picked up by the aftermarket relay and it turns your lights on. Let me know if you have any more questions.
I'm deleting your post from "under the hood" because it doesn't need to be in both places.