They can certainly work seamlessly together using some internet-based messaging services, and there are SMS apps that have tablet versions that allow you to pair with a phone (SMS can only be sent via a cellular connection or via an SMS gateway). But you are asking about Android Messages specifically. I've not used the Web service for Android Messages, but I think you access it via a browser, in which case I'd expect you can probably also use it via a browser on a tablet, but maybe someone who does use it could confirm?
Whether you can use the Messages app on a tablet I'm much more doubtful: the app uses either SMS, MMS or RCS, all of which are cellular services. And the Play Store lists it as not compatible with my tablet, which is admittedly old but it is compatible with my previous phone which is on a slightly older version of Android, so my guess is that the messages app itself probably isn't available on a tablet.