Yes, but it'll take some effort. The two frames, that is the OM .357's cylinder frame and the "modern" Bisley grip frame's screws will line up pretty good but the fit up by the "ears" will usually be the challenge. Nothing some "good ol' boy" work won't handle.
Of course, the trigger spring designs are totally different. There is a way to adapt a New Model style grip frame to the Old Model. A few images that will certainly inspire the serious converter appear HERE.
Making a OM Bisley hammer isn't too difficult. I dig out a decent OM Single-Six hammer and purchase a brand new Bisley hammer. I cut off the top of the OM hammer and cut off the top of the Bisley hammer and then make a OM Bisley hammer.
Flatgate can do that because he is a homeboy gunsmith/welder/grafter etc par excellence! For the rest of us, we use David Clements parts to get the same effect. This is a Om 357 flat top converted to a bisley 44 Special by John Gallagher. It used Clements hammer and trigger.