In "Are you staff?" does "staff" need to be preceded with an article?

I think that it sounds more natural to say

"Are you on staff?"

Or, as @MattGibson points out, since staff is a collective noun it also sounds natural to say

Are you on the staff?

If you ask, "Are you a staff?" then it sounds as if you are asking whether the person is a long stick of wood. You could, however, say "Are you staff?" This is pretty informal, though.

If you want to make your question more specific by asking whether they are a member of the ABC staff, you can ask:

Are you on ABC staff?

Are you an ABC staff member?

Are you ABC staff?

The last is pretty informal, but should be understood by most native English speakers. It may not sound correct to their ear, though. To be on the safe side, it is best to add a preposition (are you on staff) or to fully clarify that the noun is staff member.

Just staff without the article is the correct form:

Are you staff?
Everyone in a blue shirt is staff. Everyone else is a guest.

It's not informal.

I am staff.
I'm a staff member.
I'm an ABC staff member.
I'm serving as staff.
I'm serving as a staff member.

A related use is on staff, used in slightly different contexts. I find that it most often comes up at a workplace staffed by paid employees:

How many [people] are on staff here?
We have twenty [people] on staff. = We have twenty staff members.

Oh, are you on staff now?
Yes, I'm on staff, as of last week.

The staff refers to the whole group of people that are on staff:

The staff consists of twenty-one people.
The guests threw their cocktails at the staff.

The following are incorrect, or probably not what you mean:

I'm a staff. = I'm a long stick for walking or casting spells.
I'm an ABC staff. = I'm a long stick, somehow associated with ABC.

But there are some times you must infer from context:

The theatre director fired the cast from his staff.
The powerful wizard cast fire from his staff.

I would say "Do you work here?" if you want to ask if they are a member of the current organization or if you're asking if they work somewhere else "Do you work at [the] ABC?" Where "the" can be optional.

Are you staff? Are you ABC staff? Are you a member of ABC staff?

These are the options I would use.

The staff in this case is a collective noun and this is why you would not say Are you an ABC staff or Are you the ABC staff. It's not countable specific to you.