It seems that people who have used the electrolytic rust removal process have found that it leaves the bluing intact. For example: Roy Seifert and c141b.
Adding “firearm” to the search noted above gets links with greater relevancy.
This article is specifically about *removing* the bluing. The author used vinegar to remove the bluing. He *thinks* (but does not know) that the bluing, Fe3O4 (magnetite), is converted to Fe2O3 (red rust). Note that the vinegar is acidic and the soda wash solution used in electrolytic rust removal is basic. He also states that bluing is done in a solution of KNO3 + NaOH which would be basic.
As part of this article on electrolytic rust removal, a description of the chemistry of is provided. The exact chemistry is evidently complex and not fully understood. However, it appears that the rust (Fe2O3) is converted to magnetite (Fe3O4) — bluing, as part of the process. This may partially explain why bluing is not damaged by the process.