Can Berdan cases be converted to Boxer? Yes. BUT it is an extreme solution that would only make sense if there were no other alternative. EG - rare cases, not formable from any Boxer primed case or Berdan case which uses a standard, available primer; an unobtainable size of Berdan primers, etc. I have heard of caseheads being drilled and threaded, with a new pocketed insert threaded and bonded into place.
I suppose that if the case base were thick enough, a small Berdan pocket could be cut out, and a larger boxer pocket cut in. A carbide primer pocket uniforming tool would probably do this quite nicely.
For gallery loads, I have drilled out 1/4" Berdan .303 cases, and seated 209 shotgun primers; fired buckshot pellets indoors with a tiny powder charge.