In a block quotation, can I reverse the order of two sentences if I separate them with an ellipsis?

No. Sentences in a block quotation cannot be reversed because, as the MLA Handbook notes, “[a] quotation should never be presented in a way that could cause a reader to misunderstand the sentence structure of the original source” (80–81). In addition, an ellipsis is inserted in a quotation to mark when material is omitted—not if material is presented in a different order. So if you were to reverse the order of two sentences and separate them with an ellipsis, a reader would think that part of the quotation was omitted and the sentences are in sequence. 

Learn about citing quotations that are on nonconsecutive pages.

Work Cited

MLA Handbook. 8th ed., Modern Language Association of America, 2016.