Cooking of foods can make the allergenic component(s) go airborne. There
have been documented cases of people having fatal reactions to the cooking
of foods that they are highly allergic to. It's not something you want to
mess with, if you have a highly allergic person in your home.

And this last stream of responses should demonstrate that "it depends."
Depending upon a lot of factors, it is possible that some people who are
allergic to a substance may not be allergic to it in a cooked form. Some
who are allergic to milk may be able to consume sodium caseinate (e.g., in
Cool Whip) without symptoms. There are separate allergy tests for milk,
casein, etc.

There is, though the possibility that the dairy-allergic person will become
sensitized to these altered proteins and become symptomatic. It is also
possible that a person could have "sub-clinical" symptoms to these altered
proteins, with no apparent symptoms until some other allergen comes along
and reveals how much closer they are to their threshold of reactivity.

Also, do be aware that the highly allergic should not rely on a particular
food to be cooked "enough." They should have rescue medication immediately
accessible at all times, and should not "orally challenge" the cooked form
of a food that they are highly allergic to unless their allergist thinks
it's safe (even then, proceed with caution).