You can indeed use your probe to set Z zero. As you note, that is the simple and sensible way to do it when you are already using the probe for X and Y.
You do need to measure the probe's height offset, compared with the same reference tool that all other height offsets are measured.
You can do this on the TT1. You unplug the TT1 and plug in the probe, then use the normal F3/Auto Measure procedure in the Offset Library. You are right that the TT1 cannot detect the probe, as it has a ruby ball. However, the probe will trigger itself when it touches the TT1, and the control doesn't know the difference. So you plug in the probe instead of the TT1.
Just be sure to plug the TT1 back in before you go to measure any other tools!
If you want to avoid the cord swapping and the potential costly mistakes that go with it, I sell a splitter box and extension which gives you two probe sockets within easy reach in front of the machine. Leave the TT1 plugged into one socket all the time. Plug and unplug the probe in the second socket as needed. See www.cncsnw.com/products.htm.