No, not exactly, and not specifically in this case.

Natural Immunity would normally develop in most people after getting infected 4 or 5 times. However, Covid-19 is the most transmissible and fast-adapting/evolving virus in the history of science. This is mostly because it was probably engineered for maximum transmissibility. The problem with Covid is that it was so transmissible that it managed to cross the species barrier, back and forth, dozens of times. We've found lions with Covid (but not bats hilariously).

This means that when your body gets infected with one strain of covid, it can develop natural immunity to one strain. Not the dozens of additional variants. Now, people who've been infected will have an immune system that will recognize the virus and it's spike protein, so you are better off should you survive your initial infection than someone who not infected, or someone who was given the MRNA injection which only manufactured the spike protein. So, your symptoms should be lessened (that's the natural immunity), but the virus evolves so rapidly that it's impossible to stop from being infected.

I tried to warn people at the time: almost every single human being alive in 2020 was going to be infected with Covid. It's effectively impossible to stop, so the only way to inoculate the population would have been through intentional infection of the healthy.

Hilariously, this is where we go back to where the virus evolves quickly. The best reproduction strategy for any virus is to not kill the host. Evolution will actually dictate that viruses will get less lethal with exposure and adaptation, because of the benefits of keeping the host alive. As exposure became more common, the lethality of the virus would go down. This is why quarantines and lockdowns were bad, even form an immunology standpoint, you wanted to spread the infection to lessen it's lethality over time. Keep the vulnerable at home, but allow the healthy to get sick in a safe manner to build up immunity and let the virus evolve to be less deadly.

Contrast this with ebola outbreaks that kill 50% or more of infected. They kill their hosts so quickly that it becomes impossible for the host population to survive the infection. In so doing, the virus routinely exhausts it's spread in humans once an outbreak starts. You basically can't have an ebola pandemic.

I disagree with u/Filo76 because I haven't seen anything to suggest vaccinations make the immune system weaker. This one in particular just gives you a spike protein, which never immunized you from anything, but did send your body into a kind of immunological shock to fight off a bizarre protein strain. That will help your immune system deal with the Spike Protein, but little else. It doesn't prevent infection or transmission, and it was never designed to. The whole point of the genetic therapeutic was for it to help reduce hospitalizations, because people didn't know how lethal remdesivir & respirators were at killing Covid patients.