Once in Teams Only mode, the Skype for Business client will be optimized for the meeting join experience; they will not be able to chat/call. However, Teams fully supports federation, so they would be able to use the Teams client to talk to federated external users (those users could be using Teams or Skype for Business).
@Judith Schütz in addition to my good friend Bryan's accurate response, please note that older Skype for Business or Lync clients may still expose the chat and calling capabilities in TeamsOnly mode. We will progressively block these clients from being used in TeamsOnly mode. Instead customers should either upgrade their clients to the most recent ones (which provide an optimized experience) or use the Skype Meetings App to join Skype for Business meetings they are invited to.