According to evangelicals, does the use of historical criticism violate the doctrine of inerrancy?

The Wikipedia article you linked to explains that "historical" criticism involves several methodologies, including source, form, and redaction criticism, all of which are readily accepted and practiced by evangelicals.

Any seeming opposition to historical criticism is probably really more based on the non-traditionalists who call themselves "historical critics" or "higher critics" and whose conclusions include rejecting the in-text authorship of the Epistles, claiming that the Pentateuch dates to the time of Josiah or later, etc. These conclusions are often based on very thin evidence. If you haven't read the classic satirical take on the Documentary Hypothesis, New Directions in Pooh Studies, definitely give it a read. Almost everyone acknowledges that the Bible shows in many places signs of later editorial work. Many, possibly most, scholars of Genesis would say that it is a compilation of many early texts. Those texts could even have exclusively used Elohim or Yahweh. I don't think it's even out of the question that some of the texts we have now could be a translation into later Hebrew from a more ancient Hebrew (or other language) source which has been completely lost. What evangelicals don't accept is that any of these are evidence that the Jewish Law was fabricated in the time of Josiah or later, and it is conclusions like that, as well as any rejection of in-text claims of authorship, which would be considered contrary to the inerrancy of scripture. No evangelical scholar would want to ignore any evidence presented by historical critics, but they would dispute that their conclusions are reasonably derived from the evidence we have.

I think there's also a sense of the practical fruitlessness of source and redaction criticism. (Form criticism is however much more productive, as recognising and understanding text forms can reveal a lot about the intended meaning and purposes of a text.) I remember consulting a large commentary focused on source or redaction, I think in the Hermeneia series, and despite it having lots to say about the source and forms of the text, had almost no useful insights for a deeper exegetical understanding of the text, for developing theology, or for pastoral applications or preaching. Even at the best of times, these methodologies are of limited use to either academics in Biblical Studies (aside from other higher critics) or theology, or to Christians in ministry or just living as an informed God-following life. Huge amounts of scholarship gets produced based on these methodologies, but I think a lot of it is largely consumed only by academics in the same bubble that produces it.

David Clines writes:

We should therefore, in my opinion, not only be asking, Is the source analysis of the Flood narrative, or of the Pentateuch generally, true, but is it valuable? Is such a theory useful? Should I be interested in it? It is arguable that the theory, even if true, may not be very useful or very important. It might well be that scholars in a certain period might value more highly questions that are completely different: questions about the ideology of the biblical texts, for example, or about their theological value, or about their literary character, or about their characters (not excluding Yahweh), or about their effect on their readers—to say nothing of simply exegetical questions, the Pentateuch being the least and worst commented on part of the Hebrew Bible. To such questions the history of the formation of the Pentateuch may have very little to contribute. Even if the Pentateuch was composed from pre-existing sources, it is not those sources that one is studying when answering questions about the text that now exists, and that has indeed been the only text that has existed for the last two thousand years and more.

Consider that even in the Synoptic Gospels, where source criticism is perhaps most useful, while it may be able to tell us where a passage came from and how it was transformed, it gives us no certainty to why it was transformed in that way, and the author's intentions we hypothesise must fit into the purposes we see in the text read as a completed artefact. You can be a great exegete without any of these methodologies, but you can't be even a competent exegete if all you use are the methodologies of historical criticism.