The doctor usually gives a short acting sedative before the procedure. It sounds more like atrial tachycardia, not ventricular tachycardia. which would be life threatening at those rates.
I don't know which anesthesia med they use during a cardioconversion. I'm sure it's a very short acting med, probably by IV. I've never been converted that way but I think I'd want to be asleep when they do it. Ouch.