No, just no, I've heard this a million times, this theory does NOT fit the DMC timelone in the slightest, in DMC 3, the twins are roughly 18-21, and as said, in DMC 4, Nero is roughly 19-21, there's a pretty large timespan between DMC 1 and DMC 4, to make this work, Vergil would have had to have had a son at a VERY young age, and I don't know about you, but when you take biology into account, a boy that age isn't sexually mature, plus it sets a bad example for the series.
Look, here's the thing, judging by what we know of the series, it goes like this.
DMC 3: Vergil - 18-21.
DMC 1: Dante/Vergil - Mid to late 20's.
DMC 4: Dante/Vergil - Late 20's to early 30's.
DMC 2: Dante/Vergil - Mid 30's to early 40's.
Now, Nero was about 19 at the time of DMC 4, maybe a little older, it's a physical impossibility for Vergil to have fathered a child after DMC 3, as he'd become a slave of Mundus at the very end of 3, so that means he would have had to have fathered a son at a very early age for it to work, which, as I said, is pretty impossible when you take biology into effect.
So say roughly 10-12 years had to pass judging by their ages and looks at the time, from DMC 3 to DMC 4, and as Nero was roughly 19, it would mean that at the time of DMC 3, Nero would have had to have been at least 7 or 8, putting Vergil at the age of roughly 12 if he fathered Nero, therefore, rendering this theory impossible.