...I don't know how I would add reverb to the cans while tracking dry. The mic goes to the mixer and back to the phones directly and the output is recorded in the DAW. I don't know how I would give verb to the phones and get a dry track...
You just set up a cue mix (depends on what your mixer can do) and feed the reverb only to the cue mix.
You can use the Aux Send/Receive section...you can use mixer groups, send the mic to two, use one for the dry DAW out and the other to feed the headphone mix w/reverb...etc...etc.
When using outboard preamps, I send the mic signal to the pre and the pre output directly to my recording device (tape deck or DAW)...then I take the output from the tape deck or the fold-back from the DAW interface, and feed that to my mixer where I have my cue mix and where I add the reverb.
All depends on the gear and setup you are using, but there are a few ways to do it.
I do the same thing when recording guitars. I like some reverb, but I never get it from the the amp, rather I only add it to the cue mix, but the recorded guitar signal is dry. Then during mixdown I will add exactly the amount/type of reverb I want.
Everyone has their prefs...but I just find 100% dry tracks to be rather flat/dead...and somewhat unnatural sounding.
Yesterday I was listening to some You Tube clips of a local band that they recorded in their rehearsal space, and while not
a stellar rehearsal space, they recorded everything 100% dry, including the lead vocals/guitars...and it sounds so dull/blunt...the sound just dies abruptly on every word/note. Very unnatural sounding to me.