"Required" is not a good term. "Required" by whom?
If BA has an interline agreement, most likely. If not, then very unlikely as BA cannot simply issue, reissue or FIM your existing ticket to that carrier.
Nobody here knows for certain and nobody at BA will commit to this in advance. Thus, it is all about your personal risk tolerance for having something go seriously wrong with this trip and the consequences, if any, if it does,