The acid test of this statement would be to re-enact the 1940 campaign in France with Gamelin's forces replaced with the US forces of 1944, without the supporting air power. How far would Bradley/Patton be able to succeed where Weygand's counter strike never really got started?
What are the conditions that nullified Allied airpower?
Are you referring to the Fall of France in 1940 or to the historical Battle of the Bulge in late 1944?
In the Battle of the Bulge, aircraft of both sides were grounded by bad weather. Once the weather cleared, the Allies of course, were able to bring their air power to bear on the German ground forces. The Luftwaffe by that time no longer had the capability to do likewise, or to protect their ground forces defensively. The Luftwaffe shot their bolt on January 1st 1945 during Operation Bodenplatte (air strikes against Allied air fields and radar stations on the continent) and the Luftwaffe's tactical air capability virtually ceased to exist completely.
During the Fall of France, the Luftwaffe was able to establish air superiority by virtue of superior skill levels of their fighter pilots, superior air combat tactics, and a vastly superior fighter aircraft in the Messerschmidt BF-109E. The German fighter pilots had much more combat experience dating back to their experience in the Spanish Civil War. There they had developed the more modern tactics of the leader wingman element and the finger four formation. The Allies' tactics were very much behind the times at that time. It wasn't until during the Battle of Britain that the RAF started copying the German tactics.
The only Allied fighter available that could match the 109E was the Spitfire MkII. However, RAF Fighter Command was not about to risk losing their Spitfires over the continent either in air combat with more experienced German fighter pilots, or on the ground. The Allied air forces had no radar coverage there, but the Germans did.
The Allies greatly out numbered the Luftwaffe. Indeed the French Air Force alone out numbered the Luftwaffe. However, the French fighter aircraft were no match to the BF-109E. On paper the new Dewoitine D520 could, but there was only one squadron in operation. The most numerous French fighter was the MS406, but it was about 100 mph slower than the 109. Another new French fighter, the MB152, turned out to be an engineering disaster and was grounded for safety reasons. The best French fighter they had in numbers was the American Curtis Hawk (P-36). It was pretty much the same aircraft as the more famous P-40 Kittyhawk or Tomahawk (later used by the Flying Tigers in China and by the RAF in North Africa), but it used a less powerful, small, radial engine, instead of the P-40's inline Allison V-1710 engine. It was inferior to the 109E.
The Dutch had excellent aircraft, designed by Fokker, but they were in such few numbers that they were not a factor.
Having established air superiority, the Luftwaffe could support their ground forces (which the Luftwaffe was designed to do) and use their air power against Allied ground forces. Successful mechanized warfare is absolutely dependent on close air support and air superiority.