I've not seen the episode in years. In Part 2 after recovery, are there recent surgeries to his chest? If not, unlikely.
Well, any heart, even Borg-upgraded ones, would "break down" when shot. Why would the Borg use something as crude as scalpels to cut huge gashes in his chest to upgrade the heart? They could use nanoprobes, or at the very least laparoscopic surgical techniques to minimize scarring. We all know the Borg like their perfection, and scars aren't perfect!
I'm a little confused as to what the Borg would have thought upon realizing that Picard had an artificial heart. I'm not sure how much the Borg would be able to assimilate in a mechanical heart with likely simple pumping mechanisms and comparatively primitive electronics. Without knowing anything about how artificial hearts work in the future, it's hard to speculate, but I would think that the Borg would either leave it alone entirely, or completely replace it with a new mechanism. I lean towards the first option--it seems that red blood cells with nanoprobes can propel themselves, so a heart would be almost entirely redundant. I doubt drones even use their hearts in any function. In this case, it's likely that the artificial heart would have been untouched. Just my two cents.