The reason there are 7 billion (or whatever) people on earth now is that better medicine extends the lifespan, and the fertility rate has not dropped accordingly. Most especially, the effect occurs because children who, in previous eras, would have died before the age of 5 now survive into adulthood and then have children.
I do not think that preventing immune system aging would have that much of an effect, because the people whose lifespans would be increased are already beyond reproductive age, since the immune system starts its major decline after age 65.
God has numbered man’s years to 120. It won’t matter what anyone does.