Should the batter protect the runner on a straight steal?

When stealing 2nd base a point of contention exists as to whether or not you should have the batter protect the baserunner. Should the batter swing and miss intentionally to keep the catcher back and give the baserunner a better chance at stealing 2B?

There are two issues that must be weighed when making this decision.

A) Does the catcher have a slower time to 2B because the batter swung and missed?

B) If the answer to question A is yes, does it merit giving the batter an extra strike to hit with?

As for question A, I do not believe that it delays the catchers throw. A competent catcher receives the ball at the same time in the timing sequence and makes a throw to 2B regardless of whether the batter swung and missed or not. Therefore, my thinking makes letter B irrelevant. However, I'm certainly willing to concede that some coaches believe it does. Thus, making letter B a relevant discussion point.

If, in fact, swinging and missing delays the catcher, is it worth giving the batter an extra strike? I suppose it depends on the batter. Some hitters function perfectly ok with an extra strike while others become very inept in pitchers counts.

In general, I think it is overcoaching to ask a hitter to protect a baserunner who is attempting to steal 2B. They may be times when the concept applies but in general I think I would much rather my baserunner steal 2B independent of my batter swinging and missing to try and protect him.

Now, if you're having the batter do something that confuses who covers 2B. That's worth my while.