Is there a problem with adding too much Whey Protein to yogurt?

Yes. There are two primary problems:

  1. When whey proteins heat denature, disulfide cross bridging between molecules occurs and, with extreme heat, a release of sulfur also occurs. The yogurt pasteurizing step of 195° F for 8 to 10 minutes is extreme and can promote a release of sulfur. The released sulfur has been shown to interfere with a realistic yogurt aroma.
  2. In excess usage levels, whey proteins change the texture of the yogurt gel…making it more like a custard or a pudding rather than the delicate gel structure (like flan) that yogurt lovers expect. The same holds true for other stabilizers (gums, gelatins, starches, pectins).

Whey proteins do, however, impart a nice, smooth mouthfeel to yogurt and so, have found high usage in yogurt.