What sort of forces do you see them having? I think 5th Mountain is nearly a given, which pushes them up to 8 German divisions. I see the 164th division spent time in Greece in 1941-42, so probably would have been with 12th army, pushing them up to 9 German divisions. There was later 713rd static division in Greece in June, not sure if that would be used for Barbarossa beyond some occupation/security duties.
A quick count of divisions that might become available would be
2nd, 5th and 15th Panzer Division, 5th leichte Division (mot)
5th and 6th Gebirgs Division
164th Infantry Division
7th Flieger Division
You also have the following divisions that hadn't recovered from the Balkans campaign by the start of the campaign, and thus didn't enter combat until about the second half of July.
60th Infantry Division (mot)
46th, 73rd, 183rd and 194th Infantry Division
Thats a total of 12 divisions. You might add one or two static divisions and a host of other minor units as well to complement this force.
So yes, 12th army would need no help...once actually used. The problem seems to be Hitler's conceptions of the offensive, which were not influenced by the Greek/Mediterranean situation.
Then one would need to examine how determined Hitler was in his opposition to this endeavour.
One might say that the original plan was quite risky - splitting the panzer group in two, and hoping both be strong enough to link up.
Adding the DAK and associated air units to the southern pincer would greatly improve the prospects of success.
And might be enough to change Hitlers mind. Or Halders - iirc he was also sceptical of the original plan.
But as I mentioned earlier, I'm not at home at the moment, so I don't have all my sources available, and can't look into it at the moment.