Question about mipmapping and downscaling

Hello fellow gamemakers :)

I'd like to use spritemanager and make a game with a base resolution of let's say 1280x720 where I use a 1024x1024 texture for a backbround image. Now I was wondering if the renderer will automatically use a lower resolution image from the mipmap when this game is being played on, for instance, an iphone 3gs with a resolution of 480x320, so that I don't have to provide seperate resources for different resolutions?

Thanks in advance