Do you think playing to a click track makes you not a good drummer or, you can't play crazy fills and still be on with the click ? The click never lies. Most people think they have an incredible sense of timing untill put in a studio with a click, then it all comes to light that they don't. it also makes it a whole lot easier to punch and edit or, take the drums out completley and add a whole different beat or style. Some bands use the click live for video triggers and sampled things that need to be going at the exact time measures they were recorded.
As far as adding a feel to your style, I've seen AC/DC and Ramones tribute bands where the bands totally miss the style and feel of the music. Playing drums or, any instrument in a band for that matter is all about the overall feel of the band and, doing what's right for the song. It has nothing to do with drum fills or some whacked out solo. A great musician is one who knows when to do what's right for the arrangement of the song.
