DEF isn't just for soot, that's DPF (Diesel Particulate Filter). DEF is used for the SCR (Selective Catalytic Reduction) system to reduce particulate matter (soot) and emissions, particularly NOx.
The engine itself is perfectly capable of being run without DEF as it's only injected into the exhaust, but the ECM will cut power and limit you to about 5mph. They can be reprogrammed to "delete" the DEF system but it's not legal.