Sounds good like it is...
It is usually best to keep your I/O power supply separate from the ASB power supply. It should be okay to replace a faulty LVDT without turning off power to the analog card adapter module. In addition, you can remove power from the device side of the analog module without faulting it, and disconnect signal wires if necessary. Your analog readings will go to the minimum values, and the PLC will respond how it has been programmed when those values change.
If you power down the 1794-ASB and the PLC5 is still up and running, you will get a rack fault for that rack in the "S" status file in the PLC5. This is a minor fault which will not halt the processor. The PLC program will continue to run and the other I/O will not be affected.
The output image bits in the PLC5 for the affected modules will either be reset or hold their last states, depending on how you set the dip switches for the 1794-ASB.
The PLC can be configured to continually try to restore communication by setting the dipswitch for "allow processor restart". If that dipswitch is not set, the technician must initiate a reset of the rack to restore communication. When communication is restored, the rack fault bit in the PLC5 will be cleared and the module(s) in the rack will start to update again.
With some newer 1794-ASB modules, RIUP of an I/O module is supported too. (removal and insertion under power) It is even possible with these newer modules to mask the module fault status when a it's removed under power. That can be a bad thing, depending on the application. It is usually best fot the PLC program to know when a module is missing and deal with it accordingly.
What ever you do, make sure your documents for the 1794-ASB series match the actual device series. A/B has changed the functions of some of the switches over the years to support newer processors and I/O densities, so be careful there...A series "A" user manual will not apply correctly to a series "E" module.
Hope this helps,
Paul