Perhaps more than a pinch running situation: if the team goes w/ 2 catchers and one is hit with a back swing during the playoff, who would backup the remaining catcher?
That's a good question. I wonder what the rules are for replacement players when someone is hurt during the playoffs. I'd assume you can backfill from the non-playoff roster for the remainder of that series.
Edited to add; Yup:
(4) Replacements for Injured Players During a Series. A Club may request permission from the Commissioner or the Commissioner’s designee to replace on the Club’s active roster for the remainder of a post-season series a player who is unable to render service in such post-season series because of a specific injury or ailment that occurred after the Club’s roster for such series had been submitted, provided that the Club submits written proof of the disability to the Commissioner or the Commissioner’s designee. The Commissioner or the Commissioner’s designee may approve or disapprove a request for a roster substitution and may make whatever investigation the Commissioner or the Commissioner’s designee deems appropriate in exercising such discretion. The Commissioner or the Commissioner’s designee’s exercise of discretion may include disapproval of the request for a roster substitution if the Commissioner or the Commissioner’s designee determines that the request was not made in a reasonable amount of time in advance of a game to allow for investigation of the facts and circumstances. If the Commissioner or the Commissioner’s designee gives express approval for the substitution,
(A) the player added to the roster must also be an eligible player pursuant to Rule 40(a)(1) or Rules 40(a)(3)(E) through (G);
(B) a pitcher may be replaced only by a pitcher and a player other than a pitcher may be replaced only by a player other than a pitcher; and
(C) the injured player being replaced shall be ineligible to play for the remainder of such series, as well as the next subsequent post-season series that year.