It may or may not work reliably. Depends on memory quantity and speed and on graphics card power requirements.
My system is Epox 9NPA+ Ultra, AMD Athlon 64 3000+, 5x512 GEIL Value RAM, Sapphire Radeon x800gto (no separate PCIe power connector); everthing at stock speeds (no overclocking).
I attempted to use a 20-pin PSU (Antec TruePower 430), but I had problems when using 2x512MB memory DIMMs in Dual Channnel configuration (no problems if using one DIMM module only). The computer would occasionaly spontaineously reboot and then fail to POST with code C3 (copying BIOS to RAM). Memtest86+ 1.55 was failing in tests 6 and 8.
Yesterday I replaced it with Tagan TG420-U01 and the computer has been stable since. It is too soon to judge, but this may solve the problem. I will post updates.
The problem is that the 20-pin connector has only one 12V wire, which is used to supply PCIe graphics card and may be used for other components (CPU is powered by separate 4 pin connector with two yellow and two black wires). This may cause too large voltage drops when the power draw suddenly increases. 24-pin-equipped PSU has two 12V wires (all the way from the PSU to the connector) which gives less voltage drop and increases reliability.