Evidence actually speaks AGAINST this. The Chosen One does indeed have a son, but it's implied that son is now the leader of the Shark Club in Reno.
If there's any implication of a past for the Courier, it's that he could be a pure strain human somehow. He's implied to have a certain fixation with the symbols on the Divide package (Enclave) but it never gets more detailed than that.
Exactly. Although your pure strain comment is something I can't comment on. Never got the time to finish LR. Mostly because I got an interesting RP idea for a new playthrough and leapt on it.
End of the day all that's written for the Courier is involvement in NCR territory whether lounging in New Reno or a delivery gone wrong.
Other than 2 honestly 1, 3, and NV have left fairly blank slates if your playing solely as the courier with very little pre-written story. In NV other than being from the West and events from LR, getting shot in the head, etc. Even your birthplace is left up to you.
With the Chosen One's child being a Bishop and the vagueness left in the Courier's background it's no way that could be canon.
Now could YOU RP as your Chosen One's son? Go for it. But it wouldn't be canon.
I do find it strange however that in every continuing franchise people like to link past characters to new characters.
Sometimes ridiculous and a waste of time
I.E. Prison in the Arena is the prisoner in TES IV. Champion of Cyrodiil is actually Dovahkiin, Adam Jensen is technically the father of...oh wait. Heh. Nvm.
Moving on.