It just depends whether you could get a non stop path for a Voyager up the Cross City line to Lichfield and beyond.
You can easily get a path for a Cross Country service Birmingham - Lichfield - Burton that doesn’t call anywhere intermediately.
It will take approximately the same time as a cross City service from Birmingham - Lichfield, then trundle on to Burton at the low speed limit beyond. Unlikley to be much less than 50-55 minutes.