Picard has always tagged them, and if you're tagging FLAC they will go directly into the performer tag. For now, you would have to use a tool like the Tagging Tools plugin to copy them over. (That's what I'm hoping Steven will fix with the classical enhancements.)
But again, you'll also have to find a way to reformat them because the ID3 standard, and consequently Picard, uses the format "role; artist", making them separate entries. It is possible with some creative regex, I just gave up on it for a while because I had higher, less irritating, tagging priorities.