Anything is possible but consider that most people have kids out of school after June 25 and I'd think it's fare to say that the load levels will be up since everyone is travelling.
Now if you were asking about travel in January, I'd say that you're chances would be much higher!
In addition, what happens if there are only 2 seats, are you prepared to break up your trip and travel separately? Just saying since it's only once a day service...