Only if the person is already allergic to that antigen. Not if they are immune to the antigen. The word antigen refers to the protein that joins with the antibody. If the antibody is of the allergic type (IgE) then an allergic reaction will happen and if the antibody is of the immune type (IgG, IgM or IgA) then there won't be an allergic reaction.

The uses of antigen and antibody reaction will vary but are common for laboratory diagnostics. They are used to test blood compatibility through serological tests.

An Arthus reaction is a hypersensitivity reaction involving the in situ formation of antigen/antibody complexes after the intradermal injection of an antigen.

precipitation reaction

Adjuvant is a subsatance that together with antigen increases antibody reaction.