Yes, but it can also verify currently installed apps too.

Installing an app from an APK file is trust on first use. All apps are signed by a certificate from the app developer which the OS trusts. Apps can only update if it is both a newer version, and it is signed by the same certificate it came with.
 
Updates are verified by only allowing updates from that same developer's certificate. If it doesn't match, it will fail. This prevents installing a fake or malicious update.

AppVerifier checks the apps you installed are have the genuine certificate and package name from the developer. It can compare to keys you provide or it can check from an internal database of apps in the app if there is an entry for it.

DB can be found here: https://github.com/soupslurpr/AppVerifier/blob/master/app/src/main/kotlin/dev/soupslurpr/appverifier/InternalVerificationInfoDatabase.kt