R+L=J question

[blackninja9939]

Also R+L=J events still seem to be a little messy, for example Jon's parentage in his character page/family tree doesn't change after the events fire.

It only changes once he reveals it to the world
As for your initial question no but that could be a good idea however you have to remember that Ned does not actually know Joffrey is not a Baratheon for most of Joffrey's life also it is quite out of Ned's character to do so