Yes, but I can't run apps on the cloud can I? As far as I'm aware, I need them installed on the phone in order to execute them. Downloading them from the cloud and then deleting them after I'm done sounds a lot less than desirable compared to just getting a 32gb iPhone.
All you have to do is backup your iphone then do your transfer at the Apple store thing. When you get your new iPhone, type in your icloud account and it'll redownload everything back. As for deleting them, couldn't you just restore the iphone as new?