I wouldn't be surprised.
There IS a sensation in almost any theater building that's more than a few years old that performances may sort of... linger... in the space. To me at least, different stages have different vibes depending on their age and character, but any stage feels anticipatory - as if it waits for the next act - and also a bit whisper-y with past performances. This is true when sitting in one of the velvet seats in the house, but especially true in the darkness of the wings and backstage. (Way up in the catwalks? I wouldn't venture there alone without real business; it just doesn't feel like a place for tourists.)
I'm not getting all Magic 8 Ball TM here - just making an observation.
Of the theaters in Dallas Fort Worth there is only one that I've heard claims to a haunting. (There's another where haunting seems faintly possible though.) The Dallas Theater Center building - the old Kalita Humphreys - is reputed to be haunted now and then by its architect, Frank Lloyd Wright.
In a very real way his character does permeate the building - as it must any of his designs - simply because his architecture reflects so clearly his personality through his choices. A short man, his horizontal "Prairie" style of design gives the theater low-hung soffits that feel comfortable to me, but must oppress tall people. Likewise, the angled stair treads of the Kalita's narrow stairs demand that visitors Pay Attention to the Building. And their own feet. (One drink too many and many patrons have fallen down the steps. In fact the steps to the restrooms were rebuilt to the standard way years ago because so many patrons fell.) And FLW's floor plan backstage, with its rat-maze corridors and identical stairs that go to different destinations... everyone gets lost backstage at least once. Try finding the Coke machine! Twice. Dare ya.
But besides this very material kind of haunting, there are claims that Frank Lloyd Wright's shade occasionally attends rehearsals.
I haven't seen him. However the carpenter for my last show there, The Most Fabulous Story Ever Told, reports that he kept seeing in the corner of his eye a man sitting the front row - house left, 2-3 seats in from the aisle - who, whenever he really looked... wasn't there. This is where, according to other sightings, FLW likes to sit. Just watching. Very benign.
Now, where FLW ought to haunt the building is in its elevator.
There's an old story - how true I don't know - that the master refused to have an elevator in his theater, designing, instead, two switchback ramps to bring up scenery from the basement carpentry shop. (He didn't really believe in much scenery - his building should be enough.) The story goes that the elevator was installed secretly - where a second ramp was supposed to go - and hidden from the aged FLW by strategically placed scaffolding etc. during his site visits, only revealed after his death. Great story. With all due respect - the elevator IS needed, because the horrible ramp at stage right is utterly unworkable. If you could successfully roll even an office chair up that thing in the dark between scenes you'd be lucky. But FLW's posthumous disapproval may well explain why it's such a very cussed elevator.
Architect Frank Lloyd Wright does haunt that elevator - some anonymous theater crew made sure of that: "Nooooo ELEVATORS in my Theatre!!!"
Frank Lloyd Wright's face in his theater's elevator - gifted to Public Domain