Hi there,
it's an older topic, but for anyone who's interested I was crazy enough and tried it, even gone beyond the 4 HDD: I've, just like the starter of this thread, been interested in building a (free)NAS system, so a small form factor but preferring at least 4 SATA ports and an Intel NIC, as is recommended in den freeNAS documentation. What can i say, I'm pretty happy with the setup, because you actually can run 4 3.5" HDDs on that onboard SATA power connector, just like the 4 + 1 mini SATA power (for ODD) connectors on the included cable would suggest. That setup uses 4 x Seagate ST2000DM001, each rated at 8W on r/w, actually tested 6,7W by a hardware magazine, though 8W might be a peek at POST. Encouraged by this I hooked up a PCIe-SATA controller card and added 2 more 3.5" HDD, this time slightly less power-demanding ST2000DL003, actually drawing 6.3W on load. It worked!
So yes, the DQ77KB appears to merely convert with voltage regulators and uses whatever it can draw from the PSU. Even though, for it to run on a steady supply, catching load peeks, it's best to power it with a higher wattage adapter, e.g. 150W, like one Intel recommends for it's AIO on this support page: High Wattage Power Adapter Designs for AIO