I don't think he would act the same, not Picard. Take a stand against a superior? Disobey an order? Absolutely. Probably not over something as menial as shift rotation though. lol More like violating treaties, arming factions, infringing civil liberties, placing the ship & crew in imminent & immediate danger etc... You know, real objections, and in the case of wanting to rescue Picard, as a matter of protocol, he was just wrong. It was a bad call
"I'm not suggesting we trade entire star systems for 1 man's life..." Yeah, you kind of are, Billy. Declaring him a P.O.W would be acknowledging a state of war, & mouthing off at your captain about it gets you relieved. I'd have relieved him too. However, if a shuttle had happened to go missing, shortly thereafter, I might not have reported that right away.
Why the hell didn't Will go all Jim Kirk TSFS on this situation? If you really stand by your choice to break rules & save the man, you don't stop at getting your wrists slapped, & spend the rest of the ride pouting in your quarters, you go for broke. You back that shit up. At least THAT type of defiance I could respect, win or lose.