My thought is that if you put google analytics on your site while the site is new and doesn't get any traffic it looks strange if a site with no real visitors gets new backlinks daily.
Could it be that google says "him this site ain't getting any traffic but it gets 10 backlinks a day this looks unnatural let's put it into the sandbox to avoid manipulation"?
So it would be better/safer to put google analytics on your site after you are already ranking good in the serps and getting a lot of traffic.
What do you think about this? Do i have a point there or am i paranoid?