The songs purchased enter a download queue and begin downloading one at a time. The downloads are quick if you are on a good hotspot and I was able to download most tracks in under 30 seconds. There is a pause button to stop your downloads if you wish to use your bandwidth or battery life for other purposes.
The moment a song is done downloading you can switch over to the iPod application and immediately start playing it. Leaving the WiFi Music Store application pauses any current downloads which are then resumed next time you open the application, or when you next sync your iPhone or iPod Touch.

