Can an em dash be inserted in the middle of a quotation for interjection?

The words that are inside the quotation marks should be a verbatim reproduction of what was said. To put it another way, what's inside the quote marks is sacrosanct. One could say doubly so for Holy Writ.

There are some very limited interpolations allowed when translating from a foreign language.

Quotations. Aside from adjusting quotation marks and ellipsis points to conform to house style (see ...), the editor must do nothing to material quoted by an author from another source. Interpolations (in square brackets) by the author and translations by the author of foreign language material, however, may be edited for style.

-- from Chicago Manual of Style, 13th Ed, section 2.96

The United States Supreme Court has ruled in a libel case against a journalist who had placed fabricated words inside quotation marks.

Following are excerpts from the Supreme Court's decision yesterday in Masson v. New Yorker, holding that fabricated quotations may be libelous if they materially alter the meaning of what the quoted person actually said.

-- from Court Opinion Holding That Libel Rests On 'Material Change' to Quotation, NYT, June 21, 1991, A12

The quotation marks put the reader in a frame of mind in which he or she is hearing the very words of the author (or in the OP's case, good translation of what St. Luke penned). When the reader encounters the em dash within the quote, he or she has no idea that the author did not make this editorial comment.

To directly answer your question: no, the em dashes don't constitute a valid interjection within the quotation. You can't mess with what's inside the quotation marks.