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).