I tried that a couple times. It did boost my views considerably but had little, if any, effect on my likes or followers. What has worked best for me on Facebook is to post occasionally on my personal page, providing a link and saying something like, "My Late Bloomers Rock page is up to ## likes. I'd sure like to make it to 100. If you haven't liked it yet, I hope you'll check it out and maybe mention it to your friends, as well."
Doing that a couple times got me up over 100. Now I'm working on 200....