Yes it will work.
Hard to visualize how exactly you will tap into stove line, but I have done a similar thing. I ran soft copper tubing from inside the trailer, into the floor, to the Tee where water heater was connected to black propane pipe. Under the frame try keeping the soft tubing run to minimum, and cover it with 1/2" split-tubing sold in electrical isle of Home Depot.
Before soft copper pipe goes into the floor, it goes under the dinette bench - and here I installed shut-off valve and Excess Flow Auto-Disconnect Valve. The latter would shut the propane to heater if things go bad.
I installed Oly-6 permanently on the wall, you might consider the same. I like it very much and rarely use furnace anymore. Most of the time I run it a few hours before bed time, and occasionally through the night. It is "unvented" - no exhaust, so you must have 2 ventilation openings: slightly open one window and another one across, or one window and ceiling hatch. With these precautions, you will get less CO than in your home when living near a highway or a busy street.
Make sure your CO detector works, preferably install one detector in the room with heater and another one - in your bedroom.
It comes in a clear plastic bag - keep it, and cover your Oly when not in use. Catalytic pad should not be exposed to dust too much.
My biggest gripe with Oly-6 is that it has no thermostat - only 3 modes High, Med, Low. Sometimes it's warm before bedtime and then it gets cold at dawn. Starting this thing is not something you can do with your eyes closed - it takes 2 hands (2 switches), and certain succession of steps.