I bought some but now I wonder if its IP legal? The nutritional info is fine, but are they actually cooked?

I looked up the nutritional info on pearl onions compared with regular onions, the stats are pretty much the same. Cocktail onions are just pickled onions with some spices so as long as there's no sugar in the ingredients you should be fine.

That's what I thought, but want sure about the brining process and how much cooking it entailed.

No cooking! You should be good