You're saying it's possible for Vergil to fall in love, have a child, lose the woman he loves and spiral into madness all before the age of 18-19 (not sure the exact age but that is the age of the twins in DMC3)
And since Dante is estimated to be about 31 in DMC4 (this is through piecing together chronological event based on the knowledge that he's 19 in DMC3) that would mean for Nero to be Vergil's son he'd have to be about 12-13 in DMC4 according to this theory.
Now here's the thing... The creators themselves have been known to overlook chronology at times. I remember reading that one of the creators stated that Dante was approaching 40 years old in DMC4, which would obviously make it more reasonable for Nero to be Vergil's son, but then certain dates and ages wouldn't match up properly.
So basically what it comes down to is this... If anyone (namely, the creators) were so officially follow chronology, then the theory couldn't work due to unreasonable ages (I know the Japanese has a knack for portraying very young teens as older but surely there is no way Nero is supposed to be 12).
Or, the creators do what they do best and take liberties with the timeline and the story to suit their ideas then, yes, I believe that the theory technically could be made true in that sense.
So in closing.
If you're the type of fan that area about the chronology of the timeline (like myself and other diehards do) then it can't really work.
If you're the type of fan who enjoys the story regardless of that and are fine jus accepting what the creators say is legit (which I see no problem with since they are the creators after all) then it could work.
So how's that for a wall of text? Anyway just want to say I appreciate posts like this and it's these discussions that keep the community so close to me.
And if anyone comes along and reads my text wall, please tell if I've gotten something wrong or perhaps overlooked some information.