I built my cab, which has about the same dimensions as a classic arcade, except that I have 2x4 framing inside the lower portion, that wouldn't be there in a REAL cab.
Even with that extra framing taking up space, I was still able to get my tower in there WITH a subwoofer.
The only type of cab that may give you some trouble would be one that used a "reflected monitor", like Space Invaders.
Those had the monitor mounted lower than the CP, pointing straight up in the cab, and reflected it off a piece of glass, so that it appeared to be straight back behind the bezel.
That type of cab leaves the monitor bracing sitting pretty low in the cab on a stripped one.
You may have to remove/modify this bracing, and would definitely have to build your own monitor mount, on that type of cab.