My Xeon E3-1235 with 2x4GB RAM, P8B WS board (of course you will use a ITX board) and one SSD pulled 22W at idle and 106W at full CPU load (sorry, can't do the GPU load on the Linux). So 80W pico won't cut it, the original 150W PSU would be fine.
This is very close to my specs. I might still give it a go with the PicoPSU, more out of curiosity than anything, and measure it's power draw at full load. But I expect that I'll end up having to put the Antec PS back in. Or upgrade to a higher watt Pico.
Edit 1: My Scythe Shuriken definitely does not fit. I must have a different version/model.
Edit 2: There's a heap of room in this case when you remove the front panel connectors (USB etc.) and don't have to deal with the cables. The Antec PSU is back in but I think I'll wait till the new fans arrive till I do much else. I had to take the side fan out to remove the Shuriken and don't really feel like removing the motherboard to put it back in when I'll just have to do it all over again soon. I also had to cut off the power cable connector clip, on the Intel board I'm using the power connector is right up against the fans.