A logically fallacious argument, as far as I understand should always be invalid - in every possible world.
But take a kid's argument : This is true, because my father said so. On one hand it seems obviously invalid. Such an attitude is never smart (of course, I do not imply a case in which the father is known to be an expert in something, and therefore is a valid authority, but a kid's childish attitude).
However, there is a possible world in which the father of the kid is omniscient and always telling the truth. It seems a logical possibility. But, if it is a logical possibility, then one cannot argue the argument is _logically_ invalid.