Yes all current Church Audio preamps work great with the DPA 4060 series (given compatible connectors).
I would get the larger ST-9100 instead however. The fact that you have to adjust the UGLY's levels individually with a small screwdriver makes it a huge pain in the ass in my opinion. I love the ST-9100 and don't have much use for the UGLY. It would be good for acoustic, though, because you could just set it at max gain before entering the venue and leave it there.