You can slap a binoviewer on just about anything, but with just about anything, there will be compromises.
The compromise you make with an MCT with moving mirror focus is that if you don't use some kind of Barlow or Glass Path Corrector, in most cases, you will experience aperture reduction and if you do use a Barlow or Glass Path Corrector to allow full aperture, you will reduce the corresponding loss low power and true field. Without the Barlow or Glass Path, the focal length of the telescope is also greatly increased, which lowers the field size and raises the magnification.
You can do it, but if the goal is to get a good all around experience with a Binoviewer, I recommend a minimum of an 8" Newtonian and a small MCT would not by a scope I would recommend. Yes, you can do it, but the question is are you willing to accept the compromises.
Let's do a comparison. If you use the 6" f/12.5 MCT at native focal length and a 6" f/5 reflector with a 2x Barlow. With the 6" MCT, the focal length of the scope when used with the BV without a Barlow or GPC will be over 2000mm even with great effort to keep the light path as short as possible (short visual back, Baader 1.25" Prism diagonal, BV connected directly diagonal).
With the 6" f/5 reflector though, if you use a Barlow to reach focus with the binoviewer and you are working at 2.3x then the focal length will be 1725mm, so you wind up with a less expensive scope purchase that gives a wider true field and really does not weigh much more so will be comfortable on a mount of about the same size.
Again, you can binoview anything but one has to look at the compromises, and binoviewing an MCT without a Barlow is probably going to reduce some of the aperture and increase the focal length. The aperture reduction also means that the secondary obstruction size grows even larger as a percentage of aperture.
My advice then is to use a Binoviewer in a small scope, a small Newtonian is a better choice. Not only do you get a wider field when binoviewing, you get a huge increase in true field when you are not binoviewing. A 6" f/5 Newtonian is just not that much bigger and heavier than a 6" MCT to make a difference in handling or mounting.
I would only recommend binoviewing smaller refractors if the scope can work at native focal length with the BV, or it it will only be used for planet. In these small scopes, the dimming is a much bigger penalty than in a bigger scope like an 8" Newtonian. Yes, there is the same amount of dimming in the bigger scope, but the brighter starting image (for the same power) means you get a more enjoyable view.
If you choose to go with a BV in a small MCT though, I recommend the configuration I mentioned above.