Surely it will depend how it's structured. E.g. think of the football World Cup finals - all teams don't play all other teams, because they're initially divided into groups, etc.
If there were 7 entrants one would get a bye and6 would play quarter finals. So that's 3 matches so far.
Then 2 in the semi
Then 1 in the final
So I think it works even if n isn't a power of 2.