I poly choked my Saiga 12. I didn't clean it after the last outing. Not enough rounds through it to worry about it. I live in a dry climate, so rust is not a worry.
Honestly, gofastman, I don't like most American shotguns because it's very difficult, if not impossible, to disassemble them for cleaning. Crap builds up in the action and gets behind the bolt face and you can't take them apart to get it out. Shotguns are dirty, dirty guns, and the inability to properly disassemble most shotguns was one of the major deciding factors for me in getting a Saiga 12. There's no part of that gun I can't get to within 1 minute.
My advice to you is to first use the boresnake on the bore to get most of the crud out, then hit it with a good brush and patch set to get anything else it missed. Use the boresnake "wet", by dipping the head (the area between the pull string and the brushes) in the solvent. It'll save you a ton of time and effort on cleaning.