Integration between Google's Chrome OS and Android's default messaging platform - Android Messages - will be driven by a progressive web application (PWA) on the Chromebook side of the equation. That's based on newly spotted commits to the Chromium Gerrit which explicitly points to the use of the new web technology for Android Messages on Chromebook. Since the commit is marked as a 'work in progress' there's always a chance that future changes will alter the current plans and the code is nowhere near complete right now. In fact, right now the PWA works but it does not push the application to its own window or grab the Android Messages icon for use in the U.I. Moreover, at least one merge is currently in conflict with the rest of the code relating to the feature. That's directly tied in with how the newly added 'CrosSmsService' handles message-passing between the service worker and connection manager.
The former of those last two commits have already been merged, however, so it should only be a matter of time before everything works as intended and can be released via an update. With that said, the long-awaited feature will look and feel much more like a native Android app when it finally arrives if the developers continue in that direction. It should even include a messages icon on the shelf and in the Chrome OS app drawer for launching the service. PWAs essentially download a web-application or website and operate almost exactly like standalone applications. The latest cached version is pulled forward when the application registers that the installation device is offline.
In the meantime, the commits in question are just the latest in a string of commits which have pointed to the company joining the two operating systems via Google's ongoing 'Better Together' campaign. That doesn't stop with Android Messages either, although that has been a primary focus since it was discovered. Beyond SMS sharing, Better together is expected to deliver instant device tethering and smart lock features similar to those found on Android. In short, a Chromebook and an Android handset will be able to instantly recognize a connection between the two after being set up. They'll also keep each other unlocked while in proximity and connected.