Is it possible to upgrade the logic board in a Power Mac G5 1.6GHz? Mine recently died and I was thinking of trying to fit a more powerful board like the Dual Core 2.7GHz logic board into the case instead of just replacing with the same.
In general, not at all. The boards are matched to the sensors and heat sinks and the G5 line had many many revisions as the engineers presumably adjusted to the increasing thermal loads the G5 CPU would generate.
Also, are you prepared to run the thermal calibration routines to get the repaired Mac properly controlling the fans?
Personally, I wouldn't do any work at the MLB level of a G5 unless I was bored and cost was no concern. The tight space means high risk of physically bending those boards and their high sensitivity to static damage means you need to be very conscious of continuous grounding.