Migration suggestions for 2-wire smoke detectors?

I'm looking into upgrading from a 22 year old Radionics D4112. After reading the smoke alarm docs I looked at our wiring and found that we have the dreaded 2-wire kind (System Sensor 2400T). 

The docs say that if we actually have 4 wires, we can upgrade our smoke detectors to a 4 wire model. We need to replace our smoke detectors anyway, so that's not an issue.

While we do have 4 wires, one of them is bare copper (no insulation), like a ground wire.

As near as I can tell the wire is 14/3 Romex NM-B Copper Wire. All 4 wires are solid core and in a cable jacket (unshielded).  There's the bare copper wire, then red, black, and white. The red and black wires are the ones currently used. The gauge is pretty think, at around 1.7mm, which lines up with 14 gauge spec for that type of Romex.

Is it safe to use this cable as-is for a 4 wire solution? Seems like it might be safe since none of the wires can touch each other. 

Hopefully the bare wire hasn't been used a ground somewhere. I don't know why it would given that we're only using the red and black wires anyway.

Note that I haven't tried to find where the unused white and bare wires terminate. It is unclear that I can access the currently unused wires from the panel. That said, I can probably run my own 4 conductor wire from the nearest smoke through the attic.

If it turns out that a wired installation won't work, what are my options? Maybe there’s a way to leave the smoke detectors handled by the Radionics, but still integrate with the Konnected Alarm?

Failing that is there some wireless option? I've seen some people talk about using the First Alert Wireless, but I'm unclear about how the Konnected Alarm would be able to determine if the smoke detectors are firing.

Thanks in advance for any suggestions.

In case any one cares...

While I believe that I could in fact use the Romex wiring that I have, as long as the ground isn’t truly grounded, it looks like I can’t even buy 4 wire smoke detectors in my state due to code regulations.

Also, after additional thinking, I’m more interested in smart smoke detectors than I am in reusing my existing wiring for dumb detectors. I could probably repurpose my Romex for Nest (by moving to line voltage) but google has been uneven in their support for interoperability with other standards.

So, I’m getting a First Alert Z-Wave to play with in conjunction with HA. If that works, I’ll outfit the entire house that way.

I’m not expecting the smoke alarms to be integrated to the Konnected alarm panel at this stage. Instead I’ll integrate the smoke alarms at the HA level.