I don't see any reason why they wouldn't. Maybe not right away, but the 444 was being produced all the way up to shut down.
Maybe not to the modern audience, but the 1895 444 is to marlin what the 30WCF is to the 94, a class defining caliber. Unfortunately the 45-70 came back and took market share.
I had both, but still have the 444. I may get rid of it now that Hornady had discontinued the 265 gr. FP. It was a nice cartridge, but obviously this is a minority opinion or everything about and for it would be chugging along.