Are base runners always protected on a illegal pitch?

[Snocatzdad]

I see only three scenario's

#1 Runner left early. Violates LBR and dead ball out no pitch (occurs prior to illegal pitch and supercedes

#2 Illegal pitch batter doesn't put ball in play. Dead ball, ball on batter, baserunners advance.

#3 Illegal pitch batter does put ball in play. Pending result of ball in play Offense chooses result of play or ball on batter baserunners advance.

Can't be a pick off play on an illegal pitch because it's a dead ball once catcher has it.