Android won't run anything from the app as soon as you install it. An app can only set alarms, register broadcast receivers, etc. after the first time you run it manually, for example by:
- launching one of its activities from the launcher
- clicking Open in the Play Store app
- creating a home screen or lock screen widget provided by this app
- starting it from another app (via a Share action or the like)
This isn't a complete list, but it should be pretty obvious what actions start the app. If you haven't started the app, it can't have run yet, unless the author is able to exploit a bug in Android that no one else knows about.
This is very different to the situation on desktop OSes. In Windows and most GNU/Linux package managers, installing an application consists of running code provided by the app author. In contrast, Android is designed to limit what apps can do. Android itself installs the package by reading its manifest, which tells Android the name of the package and what components it contains. Android unpacks the app's files to its own private directory in internal storage, without running any code provided by the app. If the app wants to do any further setup (such as performing an anti-piracy check, or getting you to sign into a server), it can only do this when you first run the app.