GM published a document when the LML was introduced indicating that DEF usage was about 1.25% of fuel usage.
Meaning 100 gallons of fuel would be about 1.25 gallons of DEF.
DEF is injected before upstream f the dpf, but yes, it is for reduction of NOx.
The DPF catches soot, not Nox.
Regen is to burn the soot from the DPF.
Fwiw, the LMM (07.5 thru '10) was equipped with a DPF, but did not use DEF. DEF added in '11 because of the reduced permissable level of NOx, as the emission requirements tightened.
LML, (2011), also introduced the extra fuel injector into the exhaust so the 'excess' fuel for regen did did not pass thru the engine.
2018 GMC 2500 L5P CCSB 4x4 Denali - Mineral Metallic; previous '11 LML, '10 LMM and 04.5 LLY