There are some complications that can be dismissed, like
(a) the standby power is a small +5V supply, and runs some watchdog circuitry, and perhaps the system clocks. PC3200 RAM uses 2.5V. It is completely irrelevant to memory install whether 'standby' is off or not. Off is recommended, just in case wires get crossed during install.
(b) SDRAM is not a heavy consumer of power, it is NEVER necessary to upgrade the power supply when adding SDRAM.
(c) startup with a 'new' RAM configuration always does different things from normal, because there are new memory-map tables to be constructed. Even if you set the BIOS to skip long memory test, a long memory test WILL occur.
(d) immediate startup on power-connect is a normal behavior for lots of server-class machines. If it surprises you, check the BIOS settings and the battery.
There are two explanations to the odd occurrence: the memory-table build step could be not fully supporting the new configuration (look for BIOS flash upgrades and/or try another memory-slot for the big modules), or maybe the power parts on the logic board are full of dying capacitors and sometimes the good RAM fails a memory test due to noisy power.