We can't know that because it hasn't been around long enough. But as far as taking a bayesian prior, I'd start by assuming yes except in rare cases and correct your model as evidence comes in.

I'd guess that because, for the most part, that's how the previous variants behaved. Relatively robust immunity, with subsequent infections generally being rare and more mild. Since Omicron has a lot of mutations on the spike protein which is the primary antibody target, it has greater immune escape potential because the antibodies don't fit as well.

> ... preliminary evidence WHO based their recommendation on earlier this week: People who have previously had COVID-19 could become reinfected more easily with Omicron.

https://yourlocalepidemiologist.substack.com/p/omicron-updat...

If past history is any indicator, then yes.