The antibody that I purchased is mixed with a protein stabilizer, gelatin. Can I proceed with the labeling reaction anyway, without getting rid of the gelatin? Most of the antibody would still be labeled, correct?

The gelatin will compete with the antibody with regards to biotin labeling. It is strongly recommended that the gelatin be removed prior to labeling. The kit will not work as well with the gelatin present. If the gelatin (or BSA) is not removed, a mixture of labeled antibodies and proteins results. There are antibody purification columns available from other vendors.