No, only partly. While the oats do contribute some haze, they're mostly for body. The haze is a mixture of proteins from the oats (and other grains), suspended yeast (this is why NEIPAs use low-flocculating English yeasts), and suspended hop oils.
An infection probably won't happen unless you're aging the beer for long periods of time, and since IPAs aren't normally aged and should be consumed fresh, it's probably a non-issue here.
I have used oat milk before with some success. It should go into the mash, though, since it's still mostly starch.
This is another reason why oats and other flaked products should ALWAYS be mixed with 2-row (or rice hulls). The husks in the 2-row help provide efficiency with water flow. Just putting oats in a muslin sack on their own only creates a gooey and dense "dough-ball" that the water cannot penetrate. That means you're only pulling from the surface of the dough-ball, while the inside stays shielded from water access. Using some 2-row (or 6-row) prevents this.
But I guess if they say it tastes like the real thing, who am I to argue? lol