Is the app store review process shorter for apps that passed the Test Flight Beta approval process? I use Test Flight intensively to send apps for internal and external ("Beta") reviewers.

When an app is sent for external Beta reviewers, is goes through an Apple review process before these testers can access the new version.

If an beta-approved app is sent for an app store review, can I expect a  shorter approval process there?
No, at least there's no proof that going through TestFlight first will shorten the App Store review process.  

TestFlight only performs a cursory evaluation and not a larger review that's required for the App Store.  Apple indicates that TestFlight is way to "improve your app before submitting it to the App Store for review."

However, Twitter and developer forums are full of examples of apps that passed TestFlight and failed App Store review.  I often recommended developers use TestFlight to catch the 'low-hanging fruit', simple items, that cause review rejections.