Being an owner of a 444 Marlin, you feel all those 3180ft pounds in the opposite direction. High muzzle energy in a lightweight rifle does not make for a lengthy enjoyable range experience.
The Saiga's all share a common receiver and as many other parts as possible no matter the gauge. And whatever weight the conversion loses in the barrel change it probably gets right back in going to a rifle thickness over shotgun.
I can dump 10 magnum 12ga Brenneke Rottweils out of mine on the low-gas/high-brass setting and feel much less abused than any number of my other common rifle/caliber combos.
Granted, a 12ga 1oz hot-loaded slug is probably still 700 ft/lbs less than a .444 Marlin, but few of us would be dumping them as fast as we could for laughs, or at a bowling pin shoot.
But, I'd think .444 in a Saiga would be more comfortable than many common calibers in a bolt gun.