Yes, it's possible.

You can play with the same game data across multiple devices by using the account linking feature.
To access this feature, please follow these steps:

1.) Select the menu button (三) on the upper right corner of the home screen, then select [Settings].
2.) Next, select [Connect Account], then choose [Link Data].
3.) Select [Use ID to Link Account] if you already made a Link ID. If not, select [Create Link ID] and follow the on-screen instructions.

*Please beware that linking your Sonic Rumble account with Twitch will not allow you to play your game data across different devices. Please use [Connect Account] in-game to do so.