Yes, I don't think it's surprising that omicron is able to infect people again after previous infection or vaccination. If the most "recognisable" bit of the virus (the spike protein) is so different, then it will get inside us and infect us without our immune system realising what's happening and producing antibodies against it. But once there, when the immune system starts trying to fight it with the resources available (by producing the antibodies made to previous infection by a similar virus) it can be pretty quickly seen off as it's pretty similar, apart from the spike... so we're still much less likely to become seriously ill with 2x jabs, or prior infection.
Presumably if we've just made antibodies to the booster vaccine that are just there, waiting in our blood ready to go, we are much less likely to get infected than if the antibodies have gone and we have to rely on the rest of the immune system remembering and recognising the specific virus, and then producing the antibodies against it.
I think the risk of having the vaccine or booster at the same time as covid, is that the risk of side effects is increased - from either one or the other. And I can't imagine your immune system would be too impressed at the onslaught (probably anecdotally why people having the flu jag and covid booster at the same time have felt much worse the day after than those having one at a time...) Though as you say, there must be loads of people who have been jagged with asymptomatic covid and it doesn't seem actively harmful.