Except when it doesn't stay hot.
Depends WHERE and how the P-lead breaks and on the type of magneto.
Story:
Was climbing through 6000 and noticed the MVP50 said "R Mag out" but the engine felt perfectly fine, and the run-up was normal. Precautionary landing anyway. Land, get off runway, go to idle. Ground the right mag, engine runs without an RPM drop. Ground the left mag - engine quits. Look inside cowl expecting to see shrapnel. All looks fine, except the P-lead on the right mag is broken. Put the plane away, wait till Monday. Head out to airport, and the mechanic says, "Oh I bet that it's not pushing that grounding plate inside back far enough and it's killing the mag." So we pop the back off and sure enough the end of the P-lead that presses the plate back is bouncing around inside the (non moving side) magneto.
So we got some new wire, made a couple soldered connections/shrink wrap (connection outside the mag) and put it back together. Back to normal. Here's my crude drawing of what it looks like going into the magneto (case and rest if internal wiring not drawn):
So, sometimes a broken P-lead will kill the magneto and it does not stay hot.
I have had one break and it did stay hot, but it broke outside the case and the internal bushings/washers/etc all stayed in place keeping the magneto hot. In this case the P-Lead broke at the washer - solder joint intact wire just broke near it. Close enough that the vibration caused the washer and rearmost bushing to fall and relieve the pressure against the grounding plate. When that happened it grounded the mag out and it goes cold.
Much cheaper fix than an OH/ new mag.
Edit: I don't have the model number of it, but it's a Bendix.
Edit 2: Went out and looked at it tonight, S6LN-21