Previous infection appears to be somewhat protective against symptomatic reinfection and quite protective against hospitalization upon reinfection (retrospective cohort study here, CDC summary here). This appears to be more an effect of T-cell memory rather than serum antibodies, and so far, that T-cell immunity has worked across variants. It's a bit early to say that about BA.2. but the fact that it's not a variant of concern would argue that that's the case here as well.