Yes, mead will age in the bottle. I haven't done side by side comparisons of bulk vs bottle aged mead (yet), but both will improve with age from what I have tasted.
While cork taint is real (even if a bit of a misnomer), I think it is becoming less of a problem with the cork manufacturers taking steps to prevent it. Certainly it won't be an issue with Zorks or other closures. Although synthetic corks are improving, the data I have seen suggests that they have the highest oxygen transmission rate of any of the closures.
In the wine world some make a good argument that bottling protects the wine better than a stopper in the carboy. Intuitively it makes some sense, when you look at the fact that the contact between a stopper and the neck of a carboy may only be a couple of millimeters around a large opening. Factor in that they tend to frequently loosen, and pop out, and you may very well not be protecting a batch from oxygen exposure.
Compare that to a bottle where you have a narrower opening that will have a full 1.5-2 inches of cork providing the seal, with a more positive contact with the glass, and better adherence than a stopper. Over a period of a couple of years, you may very well have a lower exposure to oxygen than with a stopper in a carboy. I haven't seen any data where this has been measured in comparison, but if anyone knows of such a study please tell me.
Fortunately, traditional (and many other) meads are much less prone to oxidative damage than wine (from all I have been able to see). I have bulk aged in carboys (and better bottles) with no obvious ill effect, however, I do most of my aging in Corny kegs which are flushed and pressurized with inert gas.
For now, the stuff I plan for long aging is still going under the longest, best quality cork I can get my hands on.