Not necessarily. Wonder trading is completely random and would match you up with a partner who's still looking for one. For example, you and your friend wonder trade at the same exact time, but other people have wonder traded too. Therefore, you partners would result into different match-ups. Plus, sometimes when I wonder trade with my friend, I would sometimes click it first, yet my friend after would get matched-up first. Wonder trading is completely random.
It is highly unlikely to do it with your friend in the friend list. The best option is to trade manually.
The only way I could see you and "Joe" trading at the same time, is if there is no one else in the trading system. People use it every day at every time - especially with different time regions across the world. When your sleeping, other are waking and wonder trading.
Hope I helped! :)
