True, but I don't think Littlefinger would do that unless he knew Jon was a threat/Jon's true parentage. Otherwise, Jon is merely just a "bastard boy with nothing to inherit."
I think he does think Jon is a threat, especially with Stannis being so close to him. Jon has a "get out of jail free" card with Stannis, and LF is smart enough to know that Stannis had to have made him the offer. If he should ever decide to give into it, then he's a huge threat to LF.
Plus if you look at his past, he not only survived the Wildings, but switched sides twice, and got both sides to join forces. That's magnificent bastardy that LF greatly prides himself on, and he was too much of a threat to leave just a few hundred miles north of Winterfell.
But I think there's no way he knows of Jon's true ancestry. He finds it too hilarious that Ned has a bastard in order to really think it through.