It does complain about them on the first launch (when the setup screen tries to sign you in for synchronization), but works perfectly after that. I was a bit surprised too. Now, my Chrome installation has been moved between 5 devices (via Titanium Backup) and still works.
The only big inconvenience is getting bookmarks to PC. There is XML file in /data/data/com.android.chrome called Bookmarks (by the way, Chrome seems to be the only Google app in com.android namespace). I just use regex to select the lines with URLs.
The only big inconvenience is getting bookmarks to PC. There is XML file in /data/data/com.android.chrome called Bookmarks (by the way, Chrome seems to be the only Google app in com.android namespace). I just use regex to select the lines with URLs.