should not be a problem, i have two 8G/1G that runs without issues on the internal.
I downloaded the .img file from Index of /releases and tried programming it to the boot partition but twrp reports "size of image is larger than target device". I remember when i installed LE on my first box a long time ago there were separate images for the 1G and 2G boxes. How did you install the new image on your 1G box? Thanks again.