No, no Goog products, No WMT, No Analytics, No site search, don't make it easy for them to f*** with your site. Especially if you are white hat there is no reason they should f*** with a site.
You can get a site search for $5/month and analytics for $1/month, no need for their products. Don't leave footprints, they will track you down and treat you like a SE terrorist. This means they will give you a -50 penalty or will ban you from their SERPs.
I know they don't owe you nothing but don't be dumb, don't make it easy for them.
I think their site reviewers all over the world are underpaid and they will kick your site whenever possible, you know this is just frustration. This is my own experience.