Can a Pokémon be in both your party and your Battle team at the same time?

Question

Is it possible to have a Pokémon be simultaneously in your party and in your Battle team? Or is it only possible for a single Pokémon to be in one place at any given point in time?

Answer 1

I can confirm that this is not possible. I tried it myself:

First, I moved my Salazzle into a PC Box and registered it to Battle Team 1, which caused an icon to appear over it to indicate that it was registered to a Battle Team.

Then, I put Salazzle back into my party, at which point the icon indicating that it was in a Battle Team disappeared.

To verify that Salazzle was no longer registered to my Battle Team, I checked the box for Battle Team 1:

Thus, a Pokémon must be in a PC Box in order to be registered to a Battle Team, however, once in a PC Box, the same Pokémon can be registered to multiple Battle Teams, as explained on the official Pokémon site:

In Pokémon Sun and Pokémon Moon, you can register Pokémon that you often use in Battle Teams, which can contain anywhere from one to six Pokémon. You can set up a maximum of six Battle Teams, and the same Pokémon can be registered to several Battle Teams simultaneously.