No, because the "operating airline" (BM) is outside Star Alliance, you can't earn or burn, or have benefits, even if you're booking on a codeshare ("marketing airline"). It's different from Oneworld, where the "marketing airline" is relevant for earn/burn.
So BRS is officially disconnected from the Star network from 29OCT. BM and LH have a very limited bilateral agreement to allow LH*G status to use the lounges at FRA and MUC when travelling to BRS on a LH (220) plated ticket using the codeshare flight numbers.