Not necessarily, if I'm listening to an album because of the artist then sure, the producer should be transparent and fade into the background. If I'm listening to an album because of the producer, I probably want to hear them add their distinctive touch. Danger Mouse, Madlib and Dan the Automator are examples of producers with very strong individual sounds and I'll make a point to listen to albums they've produced regardless of the artist or genre.

I guess listing hip-hop producers here is a bit unfair, since a large reason I listen to any given hip-hop track is because of the production, but Danger Mouse has produced rock albums that have a definitive Danger Mouse sound.

It depends. I like Steve Albini's style. Raw and live sounding but I'd still put Pixies Doolittle over Surfer Rosa, I do Nevermind for In Utero. Checkout Nina Nastasia whom Steve have worked multiple times.

That's an interesting point. I feel the same way, but Albini would argue that he doesn't have a "style". His whole concept is being a kind of anti-producer -- he sets up the audio equipment and lets the band play, and his goal is to capture the live sound as closely as possible, whatever that might be.