I would be very surprised if work would not still be going on at the BC but like I said before, I haven't received anything definite as far as schedule. Last time it took a year at each resort and to me it sounds like this is even more extensive. Again, this is just my guess.
I would not worry about staying where there is rehab going on. They only do a section at a time and most people have stayed at a Disney resort during rehab and didn't even know it. I've stayed at the BC and the Grand Floridian during major rehab and was totally unaware of it. The noise work is done only during the day when people are at the parks or pools. And if you were at any Disney resort and for whatever reason the rehab bothered you and moving you to another location at the resort didn't fix the problem (you could be allergic to a material smell they were using or something), the resort will move you to another resort if they can't accommodate you. Rehab is an ongoing thing that happens at every Disney resort every so often and like I said, most of the time you wouldn't even realize it was going on.