Technically you can participate in the tournament without buying a show ticket. UnFortunately you just won't be able to get into the show itself. The tournament actually runs before the show opens. So you can do the tournament without buying a show ticket, if that's what you want to do. The tournament is run in a separate building though so you won't even be able to see the bulk of the machines without getting a show ticket for Friday too.
The advantage to having a show ticket in addition to the tournament ticket is that you get into the show early. So as soon as the tournament is over, or as soon as you have three strikes and you're out of the tournament, you can get into the main hall early, before the show starts.