To me, the answer to posts like these are almost always clearly "no" - largely because if the answer was "yes" the question would most often not need asking. Here, however, it's a close call.
I personally would want a much better defensive catcher, and if you can trade him and get full value for him from an AL team I'd likely do it. Mitch is right, however, that the market doesn't usually value players like this as much as their production would likely warrant, so I'd be cautious of selling him on the cheap. Worst case scenario, sign/Rule 5 draft/trade for a top D no bat backup C and use defensive replacements aggressively.