There was a woman at my work who really liked Torchwood, but didn't watch Doctor Who. When Captain Jack returned to Doctor Who at the end of series 3, she happened to catch one of the episodes one Saturday evening, and on the following Monday, she asked me why the man from Torchwood had been in Doctor Who. She genuinely had no idea that Jack had originated in Doctor Who and that Torchwood was a spin-off from it. So it seems it is possible to appreciate the one without the other.