Almost went this route a number of years ago before common sense kicked in.
1) Big drawback is "IF" your suppressed barrel assembly doesn't shoot worth a crap then you are stuck with it unless you want to spend big $$$ attempting to fix it. (I don't know if replacing the barrel in an integral is ok or if that is creating a new suppressor with the involved paperwork, SOT issues) Much safer bet to just get a threaded barrel from a known good mfgr and a separate can, easier to replace a bad barrel than an integrated barrel/can. Would need an accuracy guarantee of some sort before buying, good luck with that.
2) A separate can may be used on several hosts, both pistol and rifle.
3) Cleaning of an integral might be a real challenge, carbon locked baffles might be something to research first.
4) You'll still get some port noise when the action cycles, my bolt action 22's are quieter then my 10/22 actions with the same suppressor used between them. A couple of my rifles shoot better with a suppressor attached (harmonic tuning).
I've just come across too many examples of ppl not being happy with accuracy from the integrated units to take a chance. My NFA dealer even said he wouldn't carry them anymore because of complaints of mediocre accuracy in both the Gemtech and Huntertown Arms (out of business now, IIRC) versions that he sold. I believe Orkan has a good write up somewhere about his experience with an integral and there are some more over at rimfire central.
IF overall short length is the goal, I'd just SBR the receiver and put a 6" or 10" threaded KIDD + can = 11-16" OAL.
These are all my opinions, your $ to do with what you want