It appears that I can access the logic board of the Power Macintosh G3 without unplugging the power cord like on previous Power Macintosh G3 products. Will the computer stay powered on if I open the case?

Yes, if the computer is in a powered on state and the case is opened to access the logic board, the computer will remain powered on.

Apple strongly discourages opening the case with the computer powered on. If this is unavoidable, then it should not be operated in that state for extended periods. With the case open, there is not sufficient airflow over the G3 processor and the unit could enter a thermal shutdown. Any data not saved would be lost.

Do NOT perform any upgrades to the Power Macintosh G3 with the power on. Make sure the computer is powered off and the power cord disconnected before performing any upgrade to the logic board of your computer.