I'd really be curious to see any substantial proof for that claim.
The first time pupils encounter pi isn't when measuring angles. At least over here, that's still done in degrees, which is much easier to explain, and also latches onto common cultural practice (e.g. a turn of 180 degrees). So I suppose that already makes them good engineers.
But the first time pupils encounter pi is when computing the circumference and surface of a circle. While the former would look easier with the radius (tau * r), it looks just as weird when using diameter or when using it for the surface.
I don't know of any studies yet comparing the two approaches, but https://www.tauday.com/a-tau-testimonial is the story of one student who finally "got it" when using tau instead of pi. I strongly suspect she's not unique.
If there's more data available, I don't yet know where to find it.
P.S. Yes, angles are first presented in degrees in most contexts, and understanding sines and cosines is easier when given the degree units you're familiar with. But radians do need to get introduced at some point during trig, and it's exactly the study of radians which should be done using tau (the equivalent of 360°) rather than pi (180°). Because a right angle, 90°, is a quarter of the way around the circle, and that's tau/4. A 45° angle is tau/8, one-eighth of the way around the circle. There's no need to memorize formulas when you do it this way, it's just straight-up intuitive (whereas 45° = pi/4 is not intuitive the same way).