Everyone on that ship would have been bumped up two grades, well the junior grades who have somewhere to be promoted to that isn't ridiculously beyond their actual capabilities... And since every position on that ship requires a specific rank... Lo they can't have a mere Ensign going about a mighty Lieutenants very difficult duties, they also can't have a Lieutenant wasting his (or her.) time doing the work of a mere simple dim Ensign. A mass of promotions would mean that there are no more junior officers and not enough room to retain all the new mid level officers, and the multitude rising to the flag ranks.
Taking all that as fact, which you can chose not to, Picard would probably have had to replace half his crew... Or Riker would have had to, since "crew" (human resources.) is what the bulk of the first officer's job is mostly about.