No, withdrawing Pokemon does not have any effect on your chances of hatching a Shiny Pokemon. You are free to leave and take back Pokemon as you please, as it will not affect your chances of hatching a Shiny Pokemon.
I apologise if I have misunderstood you, but based on the way you've worded your question, it sounds as if you think the amount of eggs you have hatched will alter your chance of getting a Shiny? So that it's clear, that is not the case. The Shiny chance you have is constant; it doesn't change each time you hatch a Pokemon. As far as your Shiny chances are concerned, your 600 Froakie might as well have never existed -- your chance is still as it was before. The 1/4096 chance (or whichever fraction applies for your particular situation) doesn't mean that you're guaranteed a Shiny at any point, just that you can expect on average, one Shiny per 4096 eggs you hatch.
Depending on which chance applies to your situation (1/4096 with no modifiers, 1/683 with Masuda method, 1/512 with Shiny Charm and Masuda), you might consider yourself unlucky not to have a Shiny yet. But regardless, your chance of getting a Shiny hasn't changed from the point you started hatching Froakie. It's a law of probability unfortunately.