Can a guy have an accidental orgasm or almost orgasm without touching himself?!

No.

Out is public a guy , especially a young guy in puberty can easily become aroused and although he wouldn't necessarily reach orgasm he could release some some (precum ) . Many young guys also find themselves on point of orgasm even just being close to a partner they fancy and indeed some will have a little accident and stain thier boxers

Yes, and Yes. It happens all the time. I do not envy these guys.

Once, I went to a strip show with a friend and he came in his jeans, he poured beer over it so his wife would not find out. Can you imagine!

Valerie,
It is possible but rare.
Maybe if the guy was hiding watching a couple actually go at it right in front of him. The arousal would have to be extreme for a no-touch orgasm.