Is it possible for either individual communities or Stack Exchange as a whole to vote to not proceed with the planned changes?
No. The new design is a necessary evil; the existing diversification prevented roll-out of new features, such as the site being responsive. With the reduced amount of development (wo)manpower Stack Exchange has, this was the only way to go forward. Judging by the score of the motivations post I feel that the community at least understood the reasons for this executive decision, but isn't really happy about the outcome. It's almost beginning to look like real-world politics...
My guess (but I'm not a Stack Exchange employee) is that only MathOverflow and Area 51 will keep the current designs. Area 51 is running on a very old 'version' of Stack Exchange anyway, and MathOverflow has had the right to certain exceptions from the very beginning; right now, they're still using the ancient "1.0 design".
I guess the only way to prevent the planned changes right now is to arrange a lot of money, buy the Stack Overflow company, hire some more developers and have them try to reintroduce the diversification.