It doesn't matter if you're logged in or not. After a certain amount of clicks, the cap is reached for the day and the amount of growth slows. I find that sometimes, your dragons grow quicker with less clicks. A bunch of clicks are only good for a quick burst of growth.
(Someone, please correct me if I got any of this wrong, but after watching some stalker hunts, I know that most grew faster if they weren't being clicked on tons.)