You can participate at any time during the half hour of the event, even during the last 10 seconds (though I highly advice against making it so close because of the popups and long loading times).
I've joined Dream Fest several times during its last couple of minutes, and usually lost horribly on those occasions because the opponent had already worn out my team. But also won a couple of times because of that, because the opponent figured he/she already won because I was offline, and left. Only for me to completely ruin his/her team during the last few minutes.