Re: Google to introduce HSTS accross web services soon. Any Web Gateway SSL Inspection Impact to Worry ABout?
By Google enabling HSTS, this should not cause any issues if you're using SSL inspection. This simply means that they're enforcing use of HTTPS for their sites, so even if you typed http://google.com your browser would auto-magically remember to use https (rather than getting redirected there after making a plain http request).
Google has been using https on their sites for years now, so I imagine any problems would be flushed out by now (in the MWG realm).
The potential problems I forsee would mostly reside on Google's end (as the article discusses briefly). They have to make sure their infrastructure and services is ready to handle it.