I did it for a while when I was six because I decided it would be more interesting to do it that way. It gave my teachers a bit of a worry until they asked me if there was any reason for it.
However, I was/am ambidextrous with an older half sister who was lefthanded and had experienced a lot of difficulties in school, so I think I was very strongly encouraged to use my right hand for everything. Still can't reliably/cleanly eat with a knife and fork the correct way round, though, and I would switch hands or stance during games of tennis, pool or kickboxing - I can play guitar and other stringed instruments left handed as well, just by flipping the image in my head of what the chord shapes should be. I can read mirror and upside down writing easily, too - but I do prefer to read text on a pale coloured background (I prefer green or palest primrose yellow) than on pure white.
The difference was that I could/can switch easily. I think if there is a potential difficulty, your DS would struggle to do this and wouldn't be able to hold a pencil and write with his left hand.
Strangely, DP is very similar. He's lefthanded to write, has beautiful handwriting, but for many things, he uses his right instead, as that's how he's learned many skills.
Never stopped him getting a degree without any diagnosis or intervention - the only real difficulty with him is that he has about five different directions he goes in - up, down, forward, back and to the right - in response to 'your keys are on the floor to your left hand side'.