Does immunity increase if you get infected after being double vaccinated?
Still being characterised, but not the best way to attempt to improve immunity. There's no sure fire way to know whether you would be asymptomatic, symptomatic or severely ill. Correlates of protection are still being developed and understood (with a view to accelerating approval of redesigned and new generation vaccines from phase 2 immunogenicity data rather than lengthy, large scale phase 3 efficacy trials).
Generally: immune response in such a situation can vary widely from person to person and with a number of factors (not least - degree of seroconversion post-vaccination, time after second dose, variant, age, gender, circumstances of exposure: duration, viral load).
In most cases your circulating antibody levels should climb (though after recent vaccination they might well be quite high anyway), and then, over time they will drop. Cellular response could broaden further, as the weeks and months pass, and perhaps offer further protection to disease from future variants.
But on the other hand, there will be circumstances where this doesn't happen - you might be in the minority with poor seroconversion post-vaccination (for some reason: poor response to the vaccine, immune disease or dysfunction, immune suppression). So you might develop disease, severe even and maybe worse.
It's far better, less of a gamble, to acquire and boost immunity through vaccination rather than by encountering the live virus itself. Less risk to yourself and less risk to others (you can't infect others when acquiring further degrees of immunity, via vaccination, to this particular virus with the vaccines available).
e2a: And just this morning noticed a preprint touching on this. A study looking into longitudinal immunity in vaccinated healthcare workers, for the purposes of understanding if/when boosters might be needed, noted a significant jump in circulating antibodies where infection occurred post-vaccination.
