No, No, No.
Your primary line of defense your body has to infection is your skin/mucosa/other external protection (the hairs lining your nose, your lungs mucus and cillary ladder, saliva) that block 99% of all pathogens from even entering your body.
After that you have your immune system infantry, the inate immunity response (neutrophils, basophils, eosinophils, NK cells) that can usually sense when something is not part of you and destroy it on contact. This is not a targeted response, and things slip through but a vast majority of invaders who slip into your body are destroyed before your secondary immune system is activated (get it, the inate immune system is your primary immune system because it does a majority of the work.)
Finally if a pathogen is able to evade the inate immune system the secondary immune system is there, this includes Antibodies, all types of T-cells, and all types of B-cells/Plasma Cells. Antibodies are made by plasma cells, plasma cells are transformed B-cells who have essentially just become antibody making machines. Helper T-cells are the support staff who help activate b-cells, direct the inate immune system to target certain known pathogens, and Killer T-cells are assassins who seek out and destroy known threats in a targeted way. They all work together and can’t exist without the other (as all of these cells when activated will cause a synergistic activation of the other lines.) One part of your secondary immune system is not superior to another part, and for proof you only need to look at how HIV destroys your immune system. HIV only infects Helper-T cells, it doesn’t kill any other immune cell line but if left unchecked it will completely destroy practically every helper T-cell in your body. When that happens, you lose your entire secondary immune system, and when that happens that is when you are diagnosed with AIDS (Acquired ImmunoDeficiency Syndrome.)
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