I don't believe it works that way.It raises antibodies by eliciting an immune response. Runny nose, coughing, fever, inflammation, etc are all immune responses as well. Did you think you would get the anti bodies without the rest of the immune reaction?
Do you get all the symptoms of measles, mumps, diphtheria, small pox, tetanus, rubella, meningitis, shingles, rabies etc. when you get a shot for them?
Of course not. Your body can and DOES build antibodies without producing all the symptoms of the disease.