Bulldog, a ‘block’ of a kick attempt (as defined) up to three yards beyond the NZ is simply ignored. As though it didn’t happen. Whether or not illegal touching (by A) comes into play depends on where the ball lands on the ground, or is thereafter touched by any player (or an official). Until the kicked ball touches something beyond the NZ, then illegal touching does not apply. If the kicked ball fails to cross the NZ - for any reason - the ball is alive and in play, and both teams may touch, catch, or recover the ball, and advance it (if the ball doesn’t otherwise become dead).
Some folks will tell you that “it isn’t a kick until it crosses the NZ, it is just like a fumble.” That is totally false. If that were true, then we couldn’t have running into/roughing the kicker if the kick fails to cross the NZ, and we know that isn’t true. Also, if the kicked ball goes OB without crossing the NZ, the ball belongs to Team B, regardless of the down number at the snap. That would not be true for a fumble.
Keep in mind that touching (deliberate or incidental) of the kick in/behind the NZ by Team A means that, by rule, a field goal attempt can not score, even if the ball manages to fly over the crossbar and between the uprights of B’s goal. So, if a low FG attempt kick strikes a Team A player’s helmet, shoulder, etc., it can’t score.
Once the kicked ball touches something beyond the NZ, then Team A may not touch the ball until it is touched by Team B, even if the ball rebounds behind the NZ. That is illegal touching. Once Team B touches the ball beyond the NZ (or after it has otherwise crossed the NZ), Team A may legally catch/recover the kicked ball, but they may NOT advance it after catching/recovering it.
I wish I could make it simpler, but is just isn’t simple.