Even if the majority did follow, there would be a lag of a few days at least. The swap of mining BTC to Bitch was almost instant.
The pools will have programs that automatically switch to the most profit on a near instant basis. And you can bet the pools Bitmain controls offers the best iterations.
I don't mine anymore but there is no way I would point my miners at a pool that switched to Bitch. If anyone is still using any of the Chinese mining pools, this should be a wake up call. I think a lot of people have already realized this which is why Slush pool has been growing.