Yes. The same save data can be accessed on both the Nintendo Switch version and mobile version of Pokémon UNITE.
In order to access the same save data on both versions of Pokémon UNITE, you will need to log in with a linked Nintendo Account or a linked Pokémon Trainer Club account when using a new device to play existing Pokémon UNITE save data.
Please note that when you open Pokémon UNITE for the first time on a new device, starting a new game without linking an account will create new Pokémon UNITE save data. If this happens, you will no longer be able to access your existing save data. Always pay close attention and check all relevant information before linking an account.
For more information regarding how to transfer access to your Pokémon UNITE save data, see our article here.