Yes, it's grammatically correct, but only adjectivally.
"Well-informed" is an adjective, whereas "well informed," sans hyphen, is adverbial. Since we can discuss how well informed someone is, we know it is a matter of degrees, which means one can be more or less so. Since we would never say that John is "well-informeder" than Jake, we know we have to say it another way. As an adverb, the comparative version of "well" is "better," so one would say that John is "better informed" than Jake. Adjectivally, however, since "more-informed" is a compound word, we could appropriately say that John is a more well-informed student than Jake. That said, one might also just as well say John is a better-informed student than Jake.