Even without the Balkans operations and without the spring floods, the Germans could not have started Barbarossa substantially before June 22 because of equipment shortages. To quote Martin L. Van Creveld, *Hitler's Strategy 1940-1941: The Balkan Clue* (Cambridge University Press 1973), pp. 173-4:
Stockings and Hancock, in "Swastika over the Acropolis" while quoting Van Creveld themselves appear less certain. To quote:
"As a consequence of the speed of the Yugoslav capitulation, the duration of large-scale German military involvement in the Balkans was inevitably
set by the length of time it took to capture Greece. It was not by coincidence
that Barbarossa start date was confirmed only at the end of the Greek
campaign (late April). The invasion of the USSR could not, and would
never be launched until the successful conclusion of this campaign, and
the subsequent invasion of Crete which itself was contingent on, and an
extension of, Operation Marita. It is here, perhaps, that one might look to
the weather. After all, the late thaw of 1941 delayed the opening of the
Bulgarian passes and slowed the 12th Army’s concentration—delaying the
start of Marita, with an inevitable impact on Barbarossa. All German units
from the Balkans, in particular motorized or mechanized formations,
needed a minimum of three weeks for refitting after the campaigns in
Yugoslavia and Greece ended. So too, it would take time for the 8th Air
Corps to redeploy in preparation for Barbarossa after Crete had been taken—
and the Crete operation was approved by Hitler before the Barbarossa
start date was confirmed on 30 April. Such factors were known to
Brauchitsch and his staff in the first week of April in a way that the weather
and other equipment-related considerations could only be guessed at
or estimated. The inescapable conclusion is that it was perhaps not exclusively, but certainly primarily Operation Marita that delayed the beginning
of Barbarossa until 22 June 1941."
The other point though here is that not having a Yugoslav coup is decidedly in the favour... of the allies. Since German troops were not to enter Yugoslavia under the Yugoslav-German treaty there is neither 2nd Panzer flanking the Metaxas line to drive on Salonica nor XL corps to drive into the Monastir gap. The Germans will breach the Metaxas line, they were in the process of doing so when it got flanked, but it is going to be costlier and slower and puts the German breakthroughs way further east. This in turn means more time for the Greek army of Albania to pull back and stronger allied defences in the Aliakmon line as no redeployments to cover the Monastir gap happened. Put all of it together and you probably manage to save at least Crete and a fraction of veteran Greek troops by the time the campaign is over.