As I  understand it, the answer is no as deionized water will still have some residual ions. Having said that there are certain reagents that do not need distilled water in the makeup. This depends on there in use. The reason for the distilled water is that most of today's analytical procedures are for more sensitive than the days of wet chemistry.
Our QC and Analytical lab each had it's own quartz still for the distilled water.

You can make pure water many ways.  You need to know what impurities you water has and how they effect your process.  Distilled water can have low BP carryover and dissolved gasses.  DI and RO each have their own short comings so you need be aware.

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