I think that theory is as wrong as it is possible to be. 

Cersei is quite explicit about this:

Ned said. “How is it that you have had no children by the king?”

She lifted her head, defiant. “Your Robert got me with child once,” she said, her voice thick with contempt. “My brother found a woman to cleanse me. He never knew. If truth be told, I can scarcely bear for him to touch me, and I have not let him inside me for years. I know other ways to pleasure him, when he leaves his whores long enough to stagger up to my bedchamber. Whatever we do, the king is usually so drunk that he’s forgotten it all by the next morning.”

…Ten thousand of your children perished in my palm, Your Grace, she thought, slipping a third finger into Myr. Whilst you snored, I would lick your sons off my face and fingers one by one, all those pale sticky princes. You claimed your rights, my lord, but in the darkness I would eat your heirs.

Cersei avoided having sex with Robert, when she had to she would do so in “other ways” that would not result in children, and when that failed she would have an abortion. There was no black-haired baby, Gendry is not her baby, none of those theories made any political sense whatsoever. 

And while we’re at it, while GRRM is not a geneticist, the fact that each and every one of Robert’s bastards – Barra, Bella, Gendry, Mya, etc. – have black hair regardless of the hair color of the mother is meant to be a sign that Robert Baratheon was homozygous for black hair. 

So to those who would propound this theory, I would say: