With Select you can work using multiple devices but it won't automatically sync with the project in your other computer. You can manually sync them up though!
This is because Select doesn't hold onto or store your images, it reads from the source folder so your images stay safely where you imported them to on your computer or hard drive. When working on your projects on computer 1, the ratings and flags will be stored as XMP files.
When moving to a different device, you'll need to create the project again and connect the same folder used for your other device to continue working on them. This usually works well if your source folder is on an external hard drive that you can easily switch between the devices.
Once you're done working on your images and want to change devices, on computer 1, you will need to open up the project in Select and go to the File menu and click "Refresh Source Folder" for your updated ratings to show.