>>63938737.30 Carbine falls way too short to fit, in my opinion. It really doesn't have the necessary effective range to work, particularly when you use a shorter barrel like the Thompson did, so it'll be even shorter.
It was also a straight blowback action, which together with being like twice the required weight for the Light Rifle trials, is why it was probably never even tested. Unlike the older Winchester semi-auto rifles (.30 Carbine being derived from .32 Winchester Self Loading), the weight wouldn't be distributed out underneath the barrel, so I imagine it would perhaps have an awkward recoil impulse.
To me, it gets more interesting when you look at what Melvin Johnson was doing, necking down .30 Carbine to .22 caliber, putting out a 40gr bullet anywhere between 2800fps to 3000fps, and now you're kind of starting to get something more like an assault rifle. There were M2 Carbines converted and built for this .22 Spitfire cartridge, and it was fairly well liked in field testing, because it helped tame the jumpy recoil of the M2 and also improved its range and terminal ballistics.
Ultimately, Melvin Johnson was unable to convince the military to upgrade carbines for the new cartridge as a budget stopgap, as the M16 was underway by then, the M193 Ball load of 5.56mm cranking out a 55gr bullet at 3200fps, which is about 30% more powerful.
All that said, the .30 Carbine Thompson would probably be a fun novelty akin to a HK53 or HK51, it'd be a really loud and flashy gun to fire. Might have a better magazine than the M1 Carbine.