Will shorts work in the CMMG conversion unit?  Will they cycle or have to manually extract?

Not sure on that one. It would be iffy. The spring is stiff on the CMMG but will cycle sub sonics.
Dave

If you can get 'em in the chamber, they'll shoot; but if they feed, I'll eat my hat.
If they cycle, I'll eat your hat.
WTF do you want to shoot Shorts (asked by a guy with a dedicated .22 Short 10/22)?
If it's noise, CB Longs MAY feed ( CCI, Win, Rem).
I've manually cycled Colibri's.
If you shoot many Shorts, you'll gum up the chamber, though no damage will result, except from the OOB discharge when you drop the bolt on a LR round without cleaning the chamber.
There are Long cased loads that will duplicate any Short load you can possibly find.

Interesting...my next question was going to be about subs.

And yes, noise is the concern

Time for a suppressor. I'm working on that myself.
Suppressor formum is great place to learn

Subs with a can through the CMMG are scary quiet.

The related (non-suppressed) problem is barrel length.
Nobody wants a 20" barrel on their AR because it's not tacticool, but there's a significant difference in noise between a 16" and 20"(or longer) barrel, even with match, sub, or sub-sub ammo.
Lots of Shorts are HV or transitional, unless designated SV or SS.
Speed=pressure=noise.
"CB" designated LR cased ammo is significantly quieter than match or other "subsonic" ammo, but only minor tuning will be needed to cycle match, sub, standard. CBs require LOTS more effort/time/money.
Regular Cloibris will often lodge in a rifle bore, especially as it gets dirtier ( primer only rounds are filthy).
Super Colibri's work OK, IN MY EXPERIENCE (YMMV). Manually cycled, too. Often extract poorly. I would be interested in trying an Evo.