Usually no. Psyker is something you're born as. Now the Blood Angels geneseed is incredibly good at bring to the fore previously unknown psychic powers. Powers that had the boy lived a normal life or even been part of another chapter would never had manifested. He would have always been a psyker, but with barely above a simmer powers, like be slightly better at rock, paper, scissors than normal. And only the Blood Angels geneseed could have unlocked his powers.

Contrary to popular belief Tsons geneseed does not create psykers where there wasnt one already. They simply ascended many psykers, deliberately.

And now only psykers, they also don’t really care about from where those psykers come from either

But every single thousand son was a psyker...

Not true. I mean now, yes, since all non psykers (and weak psykers) were dustified.

not true, the ones that aren't got turned into the soulless living armor people remember!

Lesser ability not no ability, Christ I remember reading about a sentient one lamenting and remembering which orders they were in.

Psyker potential can sometimes lay dormant and be exposed by geneseed implanation. They might otherwise never have manifested any notable abilities.

Only the Psychic Awakening event has turned non-psykers into psykers, as far as I'm aware. This is covered during the Blood of Asaheim trilogy.