While we shouldn't underestimate the moral effect brought on by air attacks, actual destruction of tanks by fighter bombers was minimal. Only a few percent of the total numbers lost. The Raf came to this conclusion researching the effect of air attacks in the aftermath of the battle of the falaise pocket.
Somewhat... Allied airpower caused a very small percentage of losses from German armour and had a very bad ratio of missions : kills, however, this is largely due to the measures the Germans took to prevent this. German airpower was critical in destroying both Soviet and French armoured formations in 1940-41 and airpower could be very effective at engaging and destroying armour if poorly deployed.
Allied airpower forced German commanders to two main things - move at night (reducing the first great strength of armour, mobility) and disperse their armour, removing the critical mass at the schwerpunkt that had been such a critical factor in the German operations of early to mid war. I think that even if German armour was available close to the breaches, the fact it could not be effectively and rapidly massed would have more or less doomed any counter-attack.
It is also worth noting that Allied planning assumed a much worse case scenario than occurred, with assumptions of 30% casualties in the first wave. In other words, Omaha beach was considered to be a good outcome by allied planners. Given the significant margin of success the Allies enjoyed in Neptune I cannot see how the arrival of a few platoons of tanks could have changed the outcomes in a significant way. One of the reasons for attacking five beaches was to give some redundancy to the plan - even if some of the landings were failures due to strong defences or counter-attacks there would still have been a successful landing.
A massive counter attack by several panzer divisions might have crushed the beachhead but the Germans:
1. Didn't have a couple of spare panzer divisions
2. The ones they had were in the wrong place (Calais)
3. Even if they had been there they would have been too dispersed and too slow to respond, due to Allied airpower, to crush all of the beaches.
As a side note, both Stalin and Hitler liked to have armoured reserves that they had sole control over, and in both cases this had significant negative impacts on the functioning of their armed forces.