Your relay will require a constant supply for one state vs my latching type that only requires a small pulse to change the state. My average current draw is basically 0 off the USB port. You could use a simple RC diode circuit to reduce the hold current after it switches if that is a concern for you. They may not spec the hold current but easy enough to swag.
Do you have a clear goal in mind or just wanting to play? Just curious. Obviously you are adding variables and as we saw from realfrans, it can cause some problems. If the goal is to measure active circuits, keep in mind that square wave drive. If you just want to play with it, maybe build a T-Check to go with it. In the last video I made, I show the home made T-Check and transfer relay giving some decent results to a GHz or so.