Yes, but the response will be slower than if you still have a large amount of antibodies already there.
How much difference does it make in practice is still being researched, and the uncertainty is the cause of the conflicting recommendations for or against boosters.
High antibody titers is one reason it's very unlikely to get reinfected within 3 months.
But it's more complicated as there are multiple antibody types -- the actual infection produces antibodies in your nose that aren't produced when you get the vaccine, so those antibodies would protect even more.
I read that there are ongoing studies to administer covid vaccines intranasally to protect even better (I miiight have just reas that they were actually using one of the mRNA vaccines in existence but just putting it in your nose)
edit: I could not find the story about an existing mRNA vaccine being tested intranasally, but there are other vaccines in development that are given intranasally.
> and the uncertainty is the cause of the conflicting recommendations for or against boosters.
Imo it's more relevant that the majority of the human race is not even vaccinated twice. We have to decide, where we can safe more lives. Boosting the immune response in western countries, or giving vaccine to the poorer parts of the world.
How much difference does it make in practice is still being researched, and the uncertainty is the cause of the conflicting recommendations for or against boosters.