Yes, it can work.
I own rifles in both .404 Jeffery (Cogswell & Harrison) and .416 Rigby (Ruger #1).
I tried using an NEI 424-390 cast bullet , .424" cast diameter sized down to .417", intended for .404, in the .416. In a limited experiment, it was not successful. I also tried the RCBS .416-350 bullet paper-patched to .424" in the .404. This worked better than the previous experiment, but not terribly well.
Ross Seyfried was using JACKETED .416 bullets in the .404, patching them with both paper and teflon tape as I recall. To give the patching material some "grip" on the harder bullets, he rolled them between two files or rasps to create some 'tooth' on the surfaces. Results were not bad, and certainly would have sufficed for shooting big game at reasonable distances.
I may give that a "go" some day, but with the Barnes TSX now available in both .416 and ,423 diameters, there's really no need for such measures. However, it IS nice to know that such avenues are open if needed. Sometimes a certain amount of ingenuity can be extremely valuable.
I once chronographed a load in the .416 Rigby with the 300-grain X-bullet......2990 fps, and NO mistaking the fact that the primer had worked correctly! What a marvelous long-range elk load that would be!