In theory, can I deploy Matter protocol on my Cloud Platform? Then the Matter device (Matter node) will communicate with the smartphone (Matter controller) through the cloud when they are not on the same local network.
The whole point of Matter is to standardize the behavior of the nodes. What you're describing is non-standard behavior. Of course, your devices might do such communication additional to Matter communication, but three-point communication is currently not defined in Matter (with the exception of Matter bridges bridging to non-Matter devices).
You could build something on top of Matter, but unless you are in control of all three participants that wouldn't work afterwards and more importantly it would only work for those nodes were you built your stuff on top. For the consumer—if you are building a consumer product—that would look very weird. Any other Matter device wouldn't buy into the process of calling different nodes based on availability.
Lastly, you might fail the Matter certification by doing this.
If you don't need certification and just want to use Matter as a technological basis because you don't want to create a proprietary protocol there is nothing really stopping you. Not sure if you should call it Matter then.