That adapter will work fine. I have used the regular DVI → Composite/S-Video adapter (M9267G) many times on many different Macs.
Contrary to what has been mentioned in the comments, it is not an active adapter; it requires no external power, and PAL/NTSC resolution can be output from the iMac's graphics card. It behaves exactly as any other second screen would behave, just at rather low resolution. Performance/response time will not be an issue; there is no lag.
Regarding resolution you'll get the option to run at native 720×576 / 640×480 (depending on whether it's a PAL or NTSC TV) or a bunch of other higher resolutions, up to 1024×768 (as far as I recall). Note that these higher resolutions will be scaled to the TV's native resolution, so don't expect to be able to read 10pt text in the 1024×768 setting.
You'll also get a fun option called "overscan" which switches between scaling the image on the display so you can see a black edge around it (like a CRT computer monitor) or so the image "overscans" and runs off the edge of the display (like a CRT TV picture).
There is a thread on mac-forums.com: the first screenshot shows the resolution options you'll see.