It depends on the degree of "badness", and to some degree by the nature of the music.
Bernstein’s traversals of Beethoven’s symphonies---though not of audiophile purist sound quality---are not sabotaged to anywhere near the same degree as are those of Toscanini, which though musically magnificent are sonically pretty anemic. The sound of a symphony orchestra can really be emasculated by a poor recording.
The sound quality of Glenn Gould’s J.S. Bach’s solo keyboard works recordings---also not of audiophile caliber---are not bad enough to get in the way of his performances. Though I prefer Bach on period instruments (for which the works were, after all, written to be performed on), Gould’s brilliance cannot be denied.