Yes. Pietta does, and other repro companies did produce .44 Navies.
I bought one and it works fine. Not surprising when you consider that Sam Colt shrewdly built the 1860 Army on an 1851 Navy frame, allowing him to use all of the same internal parts.
He altered the cylinder frame with that step to accomodate the stepped and larger diameter .44 caliber cylinder, and added a longer grip frame and a longer streamlined round barrel with a new rack and pinion loading lever. Voila! A completely new .44 revolver.
Colt could simply have produced a .44 caliber 1851 Navy, but chose to update the design instead.
The .44 cylinder only needs to be larger at the ball end obviously, since a cap & ball revolver uses loose powder or paper cartridges. Also, it was the introduction of the Bessemer steel process that made a small diameter .44 cylinder possible, allowing Colt to replace wrought iron which he previously used.
The same concept allowed him to produce the Pocket Navy .36 caliber revolver on a .31 caliber Baby Dragoon frame.
Check out this duelist1954 video:
https://www.youtube.com/watch?v=GV38iQwySCs
