I think the same. Yet, it's probably no serious error (the "Kennedy-error").
However, sometimes, the use of article for titles can make a slightly difference of meaning. For example, in my mother tongue Danish, 'He is a clown' means that the person behaves like a clown whether 'He is clown' means that it's his profession.
In this case, I think that we in Danish only say 'a visitor' (with article) when we want to emphasize that it's one visitor out of several (e.g. at a museum). I think that these examples are also valid in German.
When you say "normative" I think you mean "nominative", the case usually used for the subject of a sentence? I remember this by the fact that when using "sein", you are saying both things are the same so in
"Ich bin ein Vogel"
I, and the bird, are the same thing therefore the subject, whereas in
"Ich habe einen Vogel"
I am the subject and the bird is the object
Because the word Besucher is grammatically masculine and the word Person is grammatically feminine.
The Gender of words is often arbitrary. Best to learn them along with the word -- e.g. learn die Person rather than just Person so that you will know that the word is feminine. A good dictionary will be useful here.
Can i say "Ich bin Besucher" just like when you say "Ich bin Turk"
That form is for permenant "roles" (e.g. I am a father, I am a Turk) or professions (e.g. I am a teacher).
But being a visitor is not a permanent role or profession; it's a temporary thing that you can't identify with.