Will it function on either?

I don't think so, the current version fostech requires an  m16 cut carrier. I think you will need the BFS III from Franklin Armory Binary Trigger
I am thinking of getting one for my 22 as well which will make a huge dent in my 22 stash.

I wonder if it would work with the CMMG sear trip kit.

I spoke with a Fostech rep and the unit will not work with a 15-22, but will work with a CMMG 22 kit when it has a modified CMMG full auto trip kit.

I have a PSA 22 upper (which is essentially a CMMG upper&conversion). I have the sear trip installed with no modifications. I tried it today for the first time with the Fostech trigger and it works fine in semi mode. If I set it to binary, it fires on the first pull, then fires on release, but here's the strange thing..... every subsequent shot only fires on the release of the trigger. It fires just like the single shot semi mode, but won't fire on pulling the trigger, only firing on release. I don't have the anti bounce weight installed, I wonder if that would make a difference. I'm not using the anti bounce weight since I believe it is out of spec or defective. It's very difficult to get in the conversion when installed, and it's actually rubbing(if not scraping away the anodizing on the inside of the upper. When I do have it installed and charge the bolt, it only goes about half way into battery and I need to use the forward assist to close the bolt. I've never even tried firing it with the weight installed.

I wonder if the bottom rear of the 22 LR bolt under the firing pin is hanging up on the hammer.  Some notched hammers snag on the bottom edge of the bolt.   The notched hammers were used with full auto trip in M-16.   As the bolt goes to the rear the hammer is pushed back and slides along the back edge of the bolt.  The bolt can get hung on the top of the hammer and experience the stoppage your experiencing.  You might be able to file the bottom of the bolt under the firing pin to alleviate the problem.

I really think you need the anti bounce weight to get reliable function if the bolt is not hanging up on the hammer.  The hammer might be bouncing off the sear and trying to follow the bolt forward.  The timing is very critical on blowback actions, weak ammo, heavy springs, dirt/grime can affect the reliabilty of 22 rimfire semi auto.   Getting reliable feeding with full auto rimfire can be very frustrating, there was a thread a few days ago detailing the problems trying to get a CMMG kit to work with an anti bounce and trip.   The barrel collar needs to fit properly and your rifle might benifit from a TAACOM pressure plug.

I'll have to play around and see how the mechanism of the trigger works. It's just weird that it the trigger resets enough to allow it to fire on release but not on pull. I'll definitely have to contact CMMG and get the anti bounce weight released, because there's definitely not something right with that.

Fostech with CMMG kit

The trip will have to me modified to work with that, this video should show how he got this one to work.