What does your SOP specify? If water is used, a grade of water should be established (same for other chemicals).
"Milli-Q" water is a trademark (Millipore Corporation) for an ultrapure Type I or II grade of water (https://www.emdmillipore.com/US/en/product/Milli-Q-Integral-Water-Purification-System,MM_NF-C72876#specifications).
DEPC (diethylpyrocarbonate) is a chemical used to treat standard deionized water, not a type or grade of water.
Water should be specified by a minimum grade or Type, not by a brand name. Specifying the grade of water in a method or SOP would allow you to use any water that meets the established specification. If the DEPC treated water you have on-hand meets the same specifications and grade of the water you need, then it could be substituted, but why would you introduce a specialty chemical (DEPC) to your system when only ultrapure water is specified?