I'm trying to install a T-connector to this valve but it looks like the hose isn't removable, although I'm not sure. Can someone take a look and verify?
NO, the tubing is part of the valve and not a seperate removeable piece. These valves were common (because they were cheap) a few decades ago. I have seen many where the tubing broke where it is connected to the valve, causing a suprise flood; be careful messing with it.
If you need to tee the line you will need to do it a different way. I recommend soldering a male pipe thread adapter directly to the copper, then using a threaded tee.