Plausible enough for the ship - not plausible for the film's continued characterization of Kirk as a man who actually deserves command. Because Captains who completely ignore the most basic rules of their profession and then try to keep their job by hiding and lying don't deserve command. YMMV.
Not a TOS or TOS movie fan, then?
I know Kirk's anti-authority history - but that Kirk stood up for his decisions and faced the consequences. He didn't try to sweep everything under the rug like a teenager hiding his playboys. An ability to think independently, even when that means questioning your own orders is clearly a desired quality in Starfleet captains (and rightly so, given how many insane admirals we've seen) - but when you turn that into Kirk ignoring his orders while at the same time casually trying to convince Starfleet he's doing everything by the book, that's basically saying that Starfleet doesn't even matter to him. Like its beneath him, because he clearly knows best in all things.
That's not the kind of personality you want in control of a starship.
He did sweep things under the rug. From "Flashback"...
JANEWAY: You may be right. Nevertheless, I've been studying the Excelsior logs.
KIM: What do they say?
JANEWAY: Unfortunately, they don't say anything at all.
KIM: Nothing?
JANEWAY: It would seem that Captain Sulu
decided not to enter that journey into his official log. The day's entry makes some cryptic remark about the ship being damaged in a gaseous anomaly and needing repairs, but nothing else.
KIM:
You mean he falsified his logs?
JANEWAY: It was a very different time, Mister Kim. Captain Sulu, Captain Kirk, Dr. McCoy. They all belonged to a different breed of Starfleet officer. Imagine the era they lived in. The Alpha Quadrant still largely unexplored. Humanity on verge of war with Klingons. Romulans hiding behind every nebula. Even the technology we take for granted was still in its early stages. No plasma weapons, no multiphasic shields. Their ships were half as fast.
KIM: No replicators, no holodecks. You know, ever since I took Starfleet history at the academy, I always wondered what it would be like to live in those days.
JANEWAY: Space must have seemed a whole lot bigger back then. It's not surprising they had to bend the rules a little. They were a little slower to invoke the Prime Directive, and a little quicker to pull their phasers.
Of course, the whole bunch of them would be booted out of Starfleet today. But I have to admit, I would have loved to ride shotgun at least once with a group of officers like that.
http://www.chakoteya.net/voyager/225.htm