Google’s Matt Cutts said on a Hacker News comment that those who are interested in switching their whole web site from http to https should go ahead and do that.
I spotted this comment in response to Facebook going HTTPS by default, where someone mentioned that Google may have an issue indexing HTTPS content. Matt Cutts, Google’s head of search spam, said no – they index it fine and you can “feel free to go HTTPS” at this time.
This is interesting in that we know since Google switched to HTTPS on Google search by default, that the [not provided] statistic in analytics packages have caused a lot of concerns for marketers. In theory, switching your website from http to https, should enable the referrer data to be passed from Google HTTPS to your site and analytics, if you are running HTTPS on your domain as the default.
You should keep in mind, switching your whole site to HTTPS can slow the load time of your pages and take up more processing power on your server. But if you have ample server resources you may want to consider it, especially if you site has sensitive or personal data on your users.
Sites like Google, Twitter and Facebook now default many of their services to HTTPS – so it is not just the checkout process, your bank or credit card companies anymore.
Here is an older video from Matt on HTTPS and Google:
Postscript: I’ve tested to see if Google will pass the query parameter from the default HTTPS version of Google to an HTTPS web page. Google does not pass the query parameter even from HTTPS to HTTPS, they are still stripping it off. So switching your site to HTTPS for the purpose of obtaining the query parameter will have no benefit.