In short, yes. Anyone age 13 or older can join a group if they're invited. When the group owner extends an invitation, she decides if you're invited as a "normal" group member or as the assigned group coach. If the group has a coach, you can be invited as a "normal" group member. You will be able to post messages to the group board and see who else is in the group, but you won't be able to see other player's stats like the assigned coach can.
If you are also a player, then the assigned coach will see you as a player, and be able to see your player stats.
Later, if she chooses, the group owner can decide to promote you to the assigned coach position. At that point, you will be able to see the stats of the other players in the group.