Commonwealth Campaign Questions

Does winning the commonwealth ambition count as “winning” the ambition for the purposes of other rules for each member of the commonwealth?

Specific instances: the Guardian’s objective says “if you win Tyrant or it’s not declared, advance…”

If the Guardian is a Member of the Commonwealth, and the Commonwealth ambition is declared on Tyrant and is won, does the Guardian get objective credit?

Second example.

The Planet Breaker is also a member of the Commonwealth. Their grand ambition says “No Rival wins the Warlord ambition and…”

If the commonwealth ambition is warlord, and all commonwealth members (including the planet breaker) win it, does that prevent the warlord from fulfilling the grand ambition?

Thanks!