Ofcourse it's possible. Even Mk 3 coaches have been converted into working trains. NI 450's and 150's for example. An engine can even be fitted above the floor as on some very early prototypes.
I suggested on another thread that HST cars be converted and someone said it's silly because of 'obvisious reasons' though.
Neither were converted from mark 3 carriage. The NI 450s are a mark 3 derived body bolted onto a mark 1 frame. The BR 150s are mark 3 derived, but not the same design as a mark 3 carriage. The BR 150s took the mark 3 carriage design as a starting point, then modified it significantly before construction. The structural engineering of the mark 3 carriage (the monocoque design) makes it very difficult to make any extensive modifications to the body once it has been built *only small modifications are possible without having to completely redo the structural engineering of the entire vehicle.
I still think anything can be turned into a DMU with enough effort.
You're correct in that, but there is a point where the effort required makes it a worse option than building a completely new vehicle. Some can be easily converted, others would be so expensive to convert that it's just not viable.
Anything with monocoque construction which would require significant holes cutting into the body during conversion instantly becomes a huge problem, as the new holes destroy the structural integrity, and you have to more or less start over with the engineering to restore that integrity around the new design. The other issue with a monocoque is that bolting very heavy lumps (e.g. engines) onto it can also cause severe structural problems, unless they were part of the original design, as you don't have a simple frame and body arrangement to work with (e.g. bolt an engine onto the floor, and you add stress to the body sides and roof).
Monocoque is excellent for new designs, as it pretty much guarantees the maximum strength for the weight, maximum structural integrity, but it's very limiting when it comes to making major changes later (unless those changes were specifically allowed for in the original design).