Yes, he is Vergil's son, you can deduce that by reading the DMC4 novel.
http://devils-lair.org/dmc4novel.php
Read the novel summary.
There.
I haven't read the novel, but I don't have to read it. Why? As I stated earlier, it is illogical for Nero to be Vergil's son. The time-line does not work out. Vergil would of been about 10 years old when he had sex to produce Nero. Can you see that happening? Not to mention it's the most cliché way to go about explaining Nero, if you ask me. But finally, the best thing I have to go on apart from it being illogical and cliché is this -
Important note: Morihashi Bingo was the scenario designer for DMC3 and 4 but he has now
quit Capcom and is currently working as a free lancer. This novel is one of his
free lance works so it's really up to you to decide whether the revelations in this novel are canon.
Morihashi Bingo has quit Capcom (He no longer works for them). It's his free lance work. As Vergil'sBitch stated, it's more Fan Fiction than canon. Whether or not he did work for Capcom is irrelevant, Capcom as a Company have not stated that what is in the novel is canon and true to the story.