Does analog time division demultiplexing need any additional sample and hold?
If you are going to continue to use 256 amplifiers, ADCs, etc. you will need a sample and hold that is triggered each time you activate the mux channel. One thing you'll have to pay attention to is the droop rate of the SH.

Alternatively you could now get away with a single amplifier, ADC, etc. for each group of 4 or 16 channels. You would know which channel was being sampled because you are driving the mux to select the proper channel. This would greatly reduce the system complexity if you are able to do it.

Note for any of these configurations you will now have to send several signals to your mux to select the proper channel. This means you'll need some device to handle the sequencing, and this device could also be used to handle the triggering of the SH amplifier, or the per block ADC.