Somewhat The melody of the verse is in the aeolian mode which has the same notes as the natural minor However when given its usual harmonization the verse modulates from if it were in the key of E E minor to G major and back again the chorus begins in G major and moves back to E thus the flattened th and th scale degrees arent really part of the E natural minor so much as they are part of the G major harmony to which the piece has moved  So overall I would say no The piece as usually played falls well within normal tonal practice for the minor mode modulation to the relative major key The melody of the verse itself detached from harmony however does fit the aeolian mode and the lowered th and th really are noticeable Though the aeolian mode wasnt commonly used in western music until relatively late tonality was not far off when it was finally theorized by Glareanus