Sharepoint - Google Analytics for an Intranet Site

There are few security risks linked to Google Analytics. Your SharePoint site will not be hacked because you use Google Analytics. You cannot be 100% sure, but the only "safe" way is running log processing software on-premise or use built-in Web Analytics.

However, I believe the largest risk are concerned with the legal aspect of possibly exposing internal information to third parties. For instance, the page title "X aquires Y sometime in the future" might be logged to Google Analytics. I cannot advise you here, so this is something you have to discuss with your legal department.