It did seem reckless for the period. I'm not sure what sort of evidence was needed for a criminal conviction at the time, but it would definitely have brought unwanted attention from the police. In addition, I strongly suspect that it would fall under the heading of "conduct unbecoming" so if he hadn't died he might well have been kicked out of the forces. Our Jack knew that it wouldn't be an issue but the real Jack...

Though I suspect we were all just meant to go !Woah!' and our brains were meant to turn to mush and we weren't meant to think it through, which wouldn't have been an unreasonable assumption on the writers' part.