How much? This much! (one arm pointing west, one arm pointing east)
Yes lyrics are highly important to me as a drummer. For instance, certain lines in certain songs...I will play that line softer for greater impact from the vocalist.
Example: In the song "The Weight" by The Band, the one verse goes:
Go down Miss Moses/ there's nothing that you can say/ It's just old Luke and Luke's waiting on the judgement day/ Well Luke my friend, what about young Anna Lea?/ He said do me a favor son, won't you stay and keep Anna Lea company....
I play this last line (about keeping Anna Lea company) softer and it makes for a nice mood. Why? In the song, Luke is dying. His words (even though they're spoken through the singer) need to be set apart slightly from the other lines in the verse, my opinion. Levon doesn't do this, this is my idea. Think about it, a dying man just gave permission to diddle his Anna Lea, kind of important, right? That line needs different treatment IMO. Playing slightly softer there raises the musicality a notch or 2 IMO. If I didn't care about the lyrics I would have never picked up on that. Those little nuances are huge.
I think that to be a complete drummer, you need to understand what's being said in the lyrics so you can match/reflect the mood the singer creates with your playing choices. The more you listen for, the more involved in the song you become. I really don't like reading here that lyrics don't matter, they do. The reason for the song is in the lyrics, the lyrics are the song. (dance music and mindless lyrics exempted) Not something that should be ignored IMO, quite the contrary. As a drummer, we have a direct connection to the singer, we can make or break them. Knowing what they're trying to convey lyrically is vital information when trying to play a thoughtful drum part IMO.