I'm guessing this means having the entire book online. The answer is maybe. If a child sees it and loves it, the parent might one day buy it, but there's also the old "why buy the cow when you can get the milk for free?" question. Having the book up for a short time is different, but anything posted online could be saved by someone else by screenshotting the pages.
It would be hard to track statistics for this because there is no way to rule out other variables in either direction.
You do need permission from the illustrator and author to do so though. Otherwise, it's potentially copyright infringement.