Pico PSU 20pin ATX with GIGABYTE GA-H55N-USB3

Woah, old topic but to answer your question, 20 pin is compatible with the 24 pin outlet(Carc369, your wrong here). SO yes it should totally work, just plug it in with the four pins not connected (like this)

With only the 20 pins connected, maximum draw is reduced to around 330w(well underneither the max your pico PSU can supply). With a low powered i3 you should be fine, only concern is the blu-ray drive during start-up(spin up) draw quite a bit of power, but definitely in range of the super ultra efficient Pico line.