I have a similar setup:
graphics HD6570, using catalyst-12.10.
I did nothing to configure suspend or hibernate.
To fix a related problem (TTY1-6 garbled when using fglrx), I found that adding "blacklist radeon"
to /etc/modprobe.d/blacklist.conf solved the suspend problem AND the garbed text in the TTYs.
Also, I use init3 and then run startx. I'm using the default 3.2.29-smp with an initrd that does not include the fglrx module.
I think it's pretty cool the proprietary installer gives an option to roll a distro-specific package. It actually detected Slackware, and made "fglrx-9.002-x86-1.tgz" for me.
The radeon driver is fantastic, but some stuff (megaglest for example) really runs better with fglrx.
Please note, I haven't tested hibernate, but suspend resumes well now by just tapping the spacebar.
Last edited by STDOUBT; 11-02-2012 at 08:45 PM.