Can OS X be installed on the ssd part of the fusion drive?
Yes, there's a way to install OS X on the SSD. It's called "install OS X on the Fusion Drive."

The Fusion Drive automatically puts the most frequently-used files on the SSD. When there are vital system files that your hard drive needs to access in its every waking moment, there's really no reason why the Fusion Drive would ever demote it to the HDD.