No Delay to BARBAROSSA -- But Significant Implications
Firstly, as a teaser, it is worth pointing out that Hitler himself did quite explicitly blame Mussolini's failures in Africa and the Balkans for undermining his invasion of the USSR, in his famous recorded conversation with Marshal Mannerheim of Finland in May 1942. He made mention of the permanent loss of three key divisions (to Africa), and the disruption and diversion of his airforce and panzer forces, which the Balkan and Mediterranean operations entailed, while they should have been preparing for 'Barbarossa'. He doesn't explicitly say, however, that there was a consequent delay in launching 'Barbarossa', only that he had expected the operation to begin in the spring of 1941, and that the Balkan distraction had been "very unfortunate".
Hitler also took great pains to point out to Mannerheim the fact that the German war machine was a "good weather" force, and that this had caused him to delay his campaign in the West over the winter of 1939-40, despite his desperate desire to move quickly on that front. He also spoke of the difficulties caused by excessive rain for his mobile striking forces, and also their acknowledged unpreparedness for winter combat.
So while we can see from his own words that Hitler was very good at finding excuses for the German failure to conclude the war in the USSR in 1941, your question was, what do historians think?
Historian Martin van Creveld wrote a book on this exact subject back in 1973, 'Hitler's Strategy 1940-1941: The Balkan Clue', which I believe was quite influential in establishing the claim among historians that there was no significant delay to the start of 'Barbarossa' as a consequence of the Balkan Campaigns. In researching this book van Creveld meticulously followed the preparation and positioning of the German military forces in the lead-up to the invasion of the USSR, and found that the scheduling of the re-equipping and training of forces would not have allowed them to be ready for the offensive much earlier than the historical starting point, regardless of the Balkan Campaigns. He shows that units redeploying from the Balkan Campaigns were in fact in position and ready for a start to operations even before the original 16th May 1941 deadline. Many of the forces used in the Balkans were earmarked for reserve, and so were not even required to be in position until very late in the process, and the transportation timetables were very flexible, and had been designed to operate in synchronicity with the Balkan operations.
The real cause of delay, according to van Creveld, was the result of shortages of equipment for key divisions, especially motorized and panzer forces which were to be re-equipped with captured French equipment. Some of these units were still moving forward in late May and early June 1941, and some were moved forward before their equipment had even arrived, with the hope that their equipment would be scrounged from various locations and meet them at their destination. He concludes that this problem alone would have prevented a start to operations in the East before late June 1941, and it had nothing to do with the Balkan Campaign or the weather.
However, the story does not end there...
On 17th March 1941, as British forces were disembarking in Greece in response to German moves into Bulgaria, Hitler made the decision to change the objective of Operation 'Marita', from a limited occupation of northern Greece, into a complete occupation of Greece to expel British forces from the continent. This had the effect of significantly extending the scope of the operation, requiring the use of larger numbers of German forces, for a longer period of time. This threw the synchronization between Operations 'Marita' and 'Barbarossa' into chaos. Forces of 12th Army, required for duty in Greece, which had been earmarked for operations with Army Group South in 'Barbarossa', would simply not be available for the beginning of 'Barbarossa'. This did not cause a delay in the starting date of 'Barbarossa', but it did cause a significant alteration to the operational plan for 'Barbarossa'.
The existing plan for Operation 'Barbarossa', called for Army Group South to attack into the USSR along two major axes; from Rumania, with 1st Panzergruppe, and 12th Army in support; forming an encircling pincer with an attack from 6th Army and 17th Army from Poland. The loss of supporting divisions from 12th Army due to the expanding scope of the Greek operation, led Hitler to doubt the ability of the southern pincer from Rumania to safely cross the Pruth River, and as a consequence he cancelled the attack from Rumania, and directed that 1st Panzergruppe would support the northern attack from Poland instead, creating a single-axis attack for Army Group South, without the ability to create large pincer encirclements.
This had significant ramifications for the Germans. In the historical event, the single-axis attack from Army Group South from Poland was hindered and delayed by terrain and stubborn Soviet resistance, which resulted in Army Group South lagging behind as the German Army advanced into the USSR, and exposed the right flank of Army Group Centre. It was this exposed southern flank which so worried Hitler that he diverted Guderian's 2nd Panzergruppe to Kiev from Army Group Centre during the critical month of September, when German forces should have been resting, resupplying, and building up their logistics for the next stage of the campaign. We can only speculate how things might have been different if 1st Panzergruppe had been sent racing across the southern steppes of the Ukraine, instead of winding through the Carpathian valleys, perhaps encircling Kiev from the south and finding itself, rested, replenished and poised in perfect position to continue the advance to Moscow or Rostov at the beginning of September, along with a similarly refreshed Army Group Centre.
So while there was no overall delay to the start of Operation 'Barbarossa' due to the Balkan Campaign, there were potentially far-reaching ramifications due to the diversion of key units from the planned attack. Given the effect this had, we can also perhaps revisit Hitler's criticism of Mussolini to Mannerheim in 1942, and see it as perhaps not as entirely self-serving as might have been assumed.
Hitler's Strategy 1940-41: The Balkan Clue (1973) -- Martin van Creveld
Kiev 1941 (2011) -- David Stahel
English Transcription of the Hitler-Mannerheim talk