No. Antibodies are very small proteins (~10nm in size) and therefore cannot be resolved by conventional light microscopes (the resolution of conventional microscopes is limited to ~200nm because of the diffraction of light). Plus, basically all antibodies look 90% the same and only differ from eachother in small regions. Therefore, directly visualizing the antibodies would not be a good strategy, in general, to distinguish between different antibodies.
Instead, these tests involve looking at the activity of the protein (in this case, the antibody's ability to bind antigen). The test involves placing a sample of serum from the patient onto a plate coated with antigen (surface proteins from the
Borellia bacteria that would be recognized by the antibody). If present, anti-
Borellia antibodies would bind the antigens and stick to the plate whereas other proteins and antibodies in the serum would not bind to the plate. You can then wash the plate so that only proteins bound to the antigens stay on the plate. To check whether antibodies are present on the plate (indicating the presence of antibodies that recognize
Borellia antigens), you usually add a second antibody that recognizes human antibodies (these secondary antibodies are usually from goat or rabbit). The secondary antibody would bind to the plate only if the anti-
Borellia antibodies are already bound to the plate. These secondary antibodies are made so that they are linked to an enzyme that produces a color change when a specific reagent is added.
Therefore, the test is quite simple. First you add serum to the plate, you wash the plate, add your labeled secondary antibody, wash again, then add the reagent. If the reagent does not change color, no anti-
Borellia antibodies are present in the patient's blood, indicating that the patient does not have Lyme disease. However, if the reagent does change color, you know that the patient's blood does have anti-
Borellia antibodies indicating that the patient has Lyme disease (or had the disease in the past).
These type of diagnostic tests are quite common in biochemistry and medicinal chemistry. For example, I believe many of the common tests for HIV are based on this principle. The test has a fancy name which is enzyme-linked immunosorbent assay (ELISA for short). You can read more about these types of diagnostics on wikipedia (
http://en.wikipedia.org/wiki/ELISA)