If you haven't yet signed up why wouldn't you just take up the invitation to do so? Especially if you buy Club Wolrd tickets fairly often. Sounds like you would gain status fairly easily. That said you get lounge access via the ticket.

Note too, that you only earn TP and Avios for tickets in your own name. Any other people you buy tickets for would have to sign up to BAEC separately to earn TP and Avios on their tickets. But you could also create a Household account if they are family members so you could pool the Avios.