I don't think so, at least that's not how it worked on my iPod.. Once I tapped on the Cloud icon next to the songs I wanted to listen, the songs began to download. So no, it doesn't really 'stream'... They do allow you to listen to the song you want while its downloading, but it will be stored once it finishes. You can erase the song after by swiping to the right.
If I erase it by swiping to the right will I be able to play it again say a week from now? In other words will I still see it with the cloud next to it after swiping to the right and deleting.