(Yes, you can!)
You can scan for beacons the way you normally do in your iPhone app, including in the background, and use the Watch Connectivity Framework to send the enter/exit events or scan results to your Watch app.
PS If you're hungry for more, the beta releases of watchOS 4 provide access to the Core Bluetooth framework. Since the Apple Watch has standalone WiFi, you could even fetch external content in your app, or push updates to your servers based on the Watch's activity. However, this is a beta version, so it's fine for experimenting, but not for building things you need to rely on!