Lots and lots of people think their runs are extremely predatorproof. However it is much easier to *think* that than to have it actually be *so*, and if you go browse the "Predators and Pests" section of the BYC forum you will see a consistent number of "something ate all my chickens last night" threads from people who were just *certain* nothing could get into the run.
IMHO, it is a lot better to be safe than sorry; especially in a warm climate where chickens are apt to decide to sleep in the run and therefore will be a far bigger inducement to predators than if they were out of sight out of mind.
You can do it if you want, of course, just realize it introduces extra risk.
I would not rely on an electric fence to necessarily make a run 100% safe either, btw -- all electric fences fail sometimes, for various reasons, and predators can be very very quick to notice.
Good luck, have fun,
Pat