Yes. In fact ...

From the Q&A at Chicago Manual of Style last month. All I can say is "Hell, yes."

Q. Dear CMOS Staff, in a recent issue of one of our periodicals, I altered the original lineup of the names of five coauthors appearing under the title of an article and reordered them alphabetically. One of the coauthors is unhappy with this and requests, too late, to keep the original lineup, which, I assume, implicitly establishes some hierarchy in authorship. What should be my response to the unhappy coauthor?

 

A. Your response should be groveling apologies and a promise to issue a correction in the next issue of the journal and in the online version. Name order is important to authors in certain disciplines, as it indicates who is the lead author. It is meaningful to anyone who reads the paper or sees the citation on a résumé. Sometimes employment and promotion depend on having published a certain number of articles as the lead author. This is a truly regrettable error—the kind of error that can put the reputation of your periodical into question. Please make every effort to make amends.