No, because Adopt Me functions with one account connected to one avatar to move around, you cannot play on one account using multiple devices.
If you attempt to play on one account with a different device, Roblox will remove the first device from the game with an error message that says "Disconnected. Same account launched game from different device. Reconnect if you prefer to use this device. (Error Code: 273)."
If you receive this error and you have not attempted to use a different device, your account may be compromised. Find out what to do here.
If you want to use the same account so you can play with a friend or family member, they can create their own Roblox account to join you. Roblox is free to join, and Adopt Me! is free to play.