If something is that important then you'll usually want to give the user a choice from a set of options - e.g. if the user is doing something that can destroy data without the possibility of undoing their actions then you'll want a dialogue that asks them if they're sure. That should block all other interaction because it really is important. When the user has no input though, and there's nothing they can do but click 'ok', there's no need to use an alert. Just put a message on the screen that's high enough up the page's information hierarchy that they've very likely to see it. Make it sticky (so it's there until the user dismisses it, but doesn't block other actions) if it's something that they need to confirm that they've seen.
Don't force the user to do things your way. Guide the user, sure, but let them do things their way.