iMac G3 Logic Board Replacement

Yes. You have to adjust the heat sink. You may need to get a heat sink for the 600

The 600 & 700 boards have the same form factor (shape).

The 350 & 400 boards have the same form factor (shape).

The 500 board is different from the others.

Reference:
http://discussions.apple.com/thread.jspa?messageID=8986279&#8986279
see last two entries
http://discussions.apple.com/thread.jspa?messageID=9345121&#9345121

Natey,

If I buy a logic board, will it have to have the firmware update for OS X on it?

Well maybe the seller would know.
To confirm that boot into open firmware:
http://www.netneurotic.de/mac/openfirmware.html
"You can press alt alt+of when you hear the boot chime and the OF console comes up."
When you're in open firmware you'll see the first line:
"Apple PowerMac2,2 4.1.9f1 BootROM built on ......"
The "4.1.9f1" is the firmware version, which is the latest update - 4.1.9.
Richard

spudnuty is one of the iMac g3 hardware experts.

No. You need to avoid booting into Mac OS 10.2 or later with downlevel firmware. This includes from cd/dvd. You will most likely loose the video if you do so and the repair is difficult.

For a slot loading iMac, this article indicates that you need to be running 9.1 or 9.2.x.
http://docs.info.apple.com/article.html?artnum=75130
"The iMac Firmware Update 4.1.9 will only run on iMac computers with lot-loading CD or DVD drives running Mac OS 9.1 or later from a local drive. If you are using Mac OS X you must boot from a local Mac OS 9.1 or later writeable partition (not a CD, or network disk) prior to following the update instructions."

You can download the Mac OS 9 updates from the Apple site.
http://support.apple.com/kb/HT1387?viewlocale=en_US