catcher's obstruction

[Tap]

This is a hypothetical, based on a discussion I had with an instructor at a recent clinic I attended. Fast-pitch game under Federation rules (I think ASA would be the same here). Runners on 2B and 3B, and 1 out. Neither are attempting to steal.

0-2 count. Batter swings and misses and is obstructed by F2 in the process. F2 misses ball and it rolls to fence.

I believe that it's a delayed dead ball and the runners can try to advance, and then the coach can take the result of the play or have the batter placed at 1B. After all, the winning run may score from 3B on the play. The instructor said it was a dead ball, as contrasted with obstruction of a runner. The rule book defines catcher's obstruction as a delayed dead ball, so I'm not sure how the instructor could have been correct. I think he agreed that this was true if the ball was hit, but not if the batter swung and missed.

Would it matter if the runners were at 1B and 3B and the BR was put out (i.e. no dropped 3rd strike in effect)? In other words, just like the play becomes dead when an obstructed runner is put out, I guess the same could be true when an obstructed batter is put out? And if so, I would presume that the umpire could award all baserunners the bases they would have attained but for the obstruction, i.e. if they were stealing (I know in a sqeeze situation, the runner from 3B will be awarded home).