Filevault likely isn't going to work as the Genius Bar is probably going to ask for the password to check the machine operates after opening it up, likely as a matter of procedure against future complaints.
Filevault needs a whole lot of empty space on the drive to place the newly encrypted data, if something goes wrong with a users machine, that data is not recoverable by direct access to the hard drive. Avoid Filevault, it slows down the machine and it's more trouble that it's worth.
Also iMac's hard drives are not a user removable part, which is a substantial problem in the concerns of privacy. It can be done of course and should be done if the machine is going to be discarded, Apple can/has refused to work on a machine that's been user altered.
Only the MacPro and MacBook Pro lines can one be permitted to self-remove a hard drive and then take it into a Apple Store for repair. I've done this and simply had them install a new hard drive (paid for) as part of the repair process.
What I would do is this, get two blank powered external hard drives equal too or slightly larger than the size of your internal boot drive and download a free copy of Carbon Copy Cloner (disconnect all other drives, TimeMachine etc)
http://www.bombich.com/
Simply launch CCC and clone your entire OS X boot drive/partition to each of the external drives, the default setting is perfect, all you have to do is select drive A to drive B and click Clone.
(note: CCC won't clone Bootcamp partition, just the OS X partitition with no Filevault, if you have Bootcamp, boot into Windows and make a manual copy of your files to another drive, also Winclone can be used to image Bootcamp to another drive and later restore with)
It will take some time, but it's effortless as the computer will do all the work, just turn off sleep/screensaver and let it work.
Next once that is finished, reboot the iMac holding the option key down, you can select one of the external drives to boot from, so try that with each one to test them out.
Once your satisfied, then while booted from one of the external clones, run Disk Utility and select YOUR INTERNAL DRIVE and Erase > Security Option > Zero ALL DATA, let this go for a few hours until completed.
(note: if your data is of interest to govenments/corporations/criminals, use the 7x overwrite/erase but it will take overnight)
Now your internal drive is completely wiped of all data, you have everything you need on the two external clones. Your operating system, your users folders, your programs, everything (except what was in the Trash)
To make life easier for the Genius folks and cut your wait time, disconnect all drives, simply insert the 10.6 disk that came with your iMac, reboot and hold the c key down, you'll boot from the disk and can install 10.6 right onto your erased internal hard drive. This will take about 40 minutes. Then reboot to the Welcome to Mac screen and use your same user name as before. (different password is fine). Use Software Update to get current on 10.6.8.
Thats it, take your iMac into the Genius Bar and let them do thier thing, there is no trace of you on the machine at all.
Once you get the machine back, you can choose to either
1: Install your 10.6 based programs again from fresh sources/update and then simply hook up one of the external clones and transfer files (or transfer users using Migration Assistant), not boot from the clone, simply transfer the user data you want.
This is known as a "fresh install" which people sometimes do to optimize and clean up a machine. A new OS, new copies of programs and using the old copies of files. It's more work setting things back up again, but it's clean and pristine, machine runs faster.
2: Your other option is to hold option key and boot off one of the clones, (grab any files on the new internal drive you may have made), then simply use CCC to clone B to A (reverse clone)
Reboot and your back to what you had before exactly.