Do you think Varys plans would have changed if he knew about Jon Snow?

In this we will use the version/theory in which Jon is the secret child of Rhaegar and Lyanna, not saying it is true but it will be for this creative exercise.

Varys was a man who wanted to restore the Targaryens to the throne, he says he wants a true and good ruler on the throne, altho I think he just wants a good pawn, we see he goes as faar as given Daenerys the eggs and as raising Young Griff as the supposed Aegon son of Elia and Rhaegar.

Do you think that if Varys Knew that Jon Snow was Rhaegar and Lyanna son, he would have made plans for him as well? Maybe a backup plan in case of Young Griff or Daenerys not working? Would he try to put his little birdies in Winterfell as well? Would he have given one of the eggs to Jon? Try to push him away from going to the wall? Try to manipulate him or the Starks? Or would he even try to kill the boy so he doesn't become a problem for Young Griff in the future? Lets speculate!