Can the same address lines be used for multiple multiplexers?
Yeah, that should work, but I don't think you actually need that many multiplexers.  One thing to consider is there may be some signals that can be connected to all of the ADCs in parallel.  You may be able to get away with just a couple of multiplexers instead of one for each signal.  Case in point: it looks like you have a chip select signal in there.  The whole point of a chip select signal is so you can share the rest of the wires and then just assert the chip select signal on the one chip you actually want to talk to at the moment, then cycle through all of the connected chips.  My guess is you can probably connect the start signal and probably the reset signal as well to all of the chips in parallel.  You'll probably want to use a multiplexer or decoder to drive the chip select line, though, to save on I/O pins.  

Specifically which ADC are you using?