Are you certain that the faucet doesn't have a tub outlet on the bottom of the unit? That's how it is on at least one of my showers.A faucet that features only shower and no tub spout.


Then put in the "T" but put it in as low as possible.Shower only valve :
I find it strange that the connections are male. That means you can't connect with a typical male pipe thread.Shower-only valve :
We have a better image than I came up with.Typical shower valve. Left & Right is to the water supply. (hot & cold). Up and down are outlets, and are the same.
View attachment 366083
Yes and for temperature control. Two inlets, one hot and one cold. One outlet for the mix. Next route the mix to either the shower head or the bathtub spout. I showed images but I don't have a blend valve but rather separate hot and cold. What part are you not quite understanding? The answer to your initial post is a yes.
Copper pipe can be connected with a simple compression nut (crox nut) which mates to a male.I find it strange that the connections are male. That means you can't connect with a typical male pipe thread.