Mark-
Your backing board should be the same quality as the mat window itself. Both should be acid-free for longest print life. If not, you may eventually get a yellowing of the print, particularly at the edges where the migration of the acid to the artwork will be most concentrated. Hard to say how long this might take-could be years, if you'd ever see it, but if you see the print as art and it's preservation is important, why take chances? The beveled edges of your mat window will turn yellow much more quickly on non-archival mat board.