Definitely not unrealistic at all actually. Kubo has spent his entire life training to kill. He's obviously ex-military since he spent time in the Middle East, possibly special forces if he trained insurgents there. It's a lot of luck and grit but there's been worse odds in history.
No, it's very unrealistic, I sincerely doubt that someone with Kubo's background would be accepted into Japan's military and definitely not their special forces. When I did my service I guarded an airfield not far from the Russian border, and Russia wasn't as much of a threat then as now. I was still fairly thoroughly tested beforehand.
My nephew just finished his year in service, and he went for the special forces. He had thorough background checks, psychology tests, the works. The very last thing they want is a loose cannon like Kubo. My nephew had a stable background with no problems in school or family, is a good athlete and intelligent (now studying at Cambridge). He was accepted, Kubo wouldn't have been.
OK, I don't expect this manga to be too realistic, as an example the deductive capabilities of several characters are off the charts: There's a scratch on the balcony (like on all balconies), I now understand everything! Still, the writer are going off the rails here being so infatuated with this yakuza that he gives him superhuman qualities. At this point I won't be too surprised if he finds a dragonball, uses it to cure himself and flies out of there.