From what I've read about "Caption Call," you shouldn't have any issues with FiOS Digital Voice. FDV provides voice quality identical or better than copper.
Since you already have a FiOS ONT installed in your home, you are most likely getting your phone service through that ONT. If that's what you have, switching to FDV requires no changes at all in your home. You simply get the advanced features and pricing that FDV offers.
If you actually have a copper line connected back to the central office, the Verizon tech will disconnect your home phone wires from that line at the demarcation point and then run a short wire from the ONT to the demac. This will connect your ONT to your existing home wiring.
Other than connecting the ONT to your home wiring, no changes in any of your phone equipment is required. If you have an answering machine, you might want to give FDV's Voice Mail a try. It's better than any answering machine with the ability to playback messages from the web and get them by email. It might help you to be able to play back messages through a computer headset, for example.
You may want to ask the Caption Call folks directly about FDV, although I'll be surprised if they report any issues with the service.
Good Luck.
