Does low antibody response after a covid-19 mrna vaccine still offer protection or immunity?

There is no reason to test for antibody following vaccination. Vaccination protects against symptomatic Covid-19 infection. For healthy diet: http://www.choosemyplate.gov/., exercise 30 minutes/day, drink enough water daily so your urine is mostly colorless, have safe sex, no tobacco alcohol weed or street drugs.

Which test ? The antibodies to the various vaccines differ from those of the wild covid disease. Vaccine antibodies the spike protein not the main virus, so those must be tested differently.