If you are sad and depressed and have to take medication to be "happy", can we really say you are happy?
If my car can go 200 mph, I wouldn't say I can move 200 mph. But then again drugs change you in a way that cars don't.
Of course there is the question of what is happiness and how can we objectively and empirically qualify it. So the entire question could be moot.
You can swap that for any condition and any requirement of a substance, or even a requirement not to consume a substance. I personally feel like all your question does is invalidate the use of often needed medications, treatments, or other potentially stigmatized practices by people who need those things.
If I had depression, or anxiety, and someone was basically asking if I can ever be the same as others because I need medication, I think that would hit me incredibly hard. It doesn't feel like accepting or supportive language to me.
Your diabetes/insulin example is even more interesting than mine. As a person of color with higher risk of diabetes, I have family members who are diabetic and need insulin. Would I consider my diabetic family members healthy? Do they consider themselves to be healthy? If they were healthy, they wouldn't be diabetic or need insulin. But taking insulin makes them healthy. But then if they were healthy, they wouldn't need insulin, which they do. You really gave me something to think about and maybe even talk to my family members about. Thanks.
Even more, if there is a pill to cure diabetes, is a person who takes the pill more healthy than the person taking insulin?