What's the relationship between a custom recovery and rooting?
You don't need to root your phone in order to use a custom recovery like TWRP or ClockWorkMod.

It will only root your phone if you use it to...


flash a rooted image
flash a su binary
restore a rooted backup


It is common for recoveries to offer to root when you restart, but you can just say "No" if you don't want to root.