My method of fitting doweling is to clamp the broken piece in place on bat ensuring a tight fit then drill through broken piece into bat remove broken piece and continue to drill holes in the bat to a depth of no less than 1 inch. Then glue dowelling into drilled bat holes once glue has Set apply glue onto exposed dowelling and where it is required etc fit broken piece onto dowelling cut dowels flush and clamp.
Makes absolutely no sense what so ever, and depending on how the broken bit comes out of the bat, might not even be possible.
ALWAYS fix the crack first then fit the dowels, can't imagine why you would do it any other way.... Am I missing something.