Can I replace the rear brake anti rattle clips without removing the caliper?

It's not that hard to pull the caliper off. Two bolts and that's it. You can pick up a piston compressor for pretty cheap from a local auto store. I would do it that way instead of trying to avoid taking off the caliper. I can easily change the brake pads on my car in in less then 20 minutes.

If you're only removing the pads to install anti rattle clips and reinstall the same pads, you wont have to compress/screw the piston back in unless you hit the brakes while the caliper is mounted off the disc, it may be a little fight to get back on the disc with the same pads reinstalled but i've done it on both my fronts and rears. Btw you dont have to open up the hydraulics/bleeder screw during a regular brake pad/rotor change, but it is wise to uncap the master cylinder and remove some fluid when installing new pads to reduce the chances of an overfill in the reservoir.