I just checked my own Synta made 127mm Mak. It came with a 2" back. The thread that the adaptor winds on to is M50. You can measure the thread on your own 127 to see what it is.
That is not likely to be the same type as the Celestron 127 as the baffle sizes are different, so perhaps not helpful for this particular tube. From what I can tell these are the same optical design probably made in the same factory, but not the same tubes at the point of accessory attachment from what I have read. My understanding is that the Celestrons are M44.5x1.0, although that is not firsthand knowledge.
Not sure what M50 is. While I have a thread checker with my tap and dye set, it doesn't present that option. The SCT thread is is 2"-24 from what I can tell, and that matches the 24 pitch of my thread checker from what I can tell. I doubt most folks have such a thread checker though, and that presents a problem to simple checks. AgenaAstro gives this as 2"-24 and it matches my 127 f/15 Mak and 8" SCT which have the standard SCT threads.
I want to make it clear that I am not trying to discourage use of a 2" diagonal or a reducer/corrector (which would also require an SCT adapter as well as an SCT 1.25" or 2" visual back.) I just want to make sure the OP has considered the various aspects before going this route. Think of this as a system rather than doing it one piece at a time and running into unanticipated hurdles. Going to 2" is generally not cheap unless one has many of the accessories already.
Consider this: For my old 8" SCT I didn't have to worry about focuser knob interference, clearance with the fork base wasn't an issue, and I was using a dovetail weight system for balance anyway. For the 127 f/15 Mak I already had a 2" refractor diagonal and 2" visual back (that I had been using for the 8" SCT) so it was easy to test the 127 with existing pieces. The 127 did not have a focuser problem. The ES 127 has a dovetail rather than direct fork attachment, so I had some balance options that some OTA's might not have.