I'll never forget what my teacher/mentor told me, when I made excuses for not learning the pedals: "If you're not going to play pedals, you might as well play piano."
A little over the top, sure... but it's akin to saying, "Can I be a drummer without playing the bass drum?" Sure you can. It might even be cool. But why not learn it and then if you don't want to use it that's fine but you'll still have the skills to work in multiple situations. The name of the game in the gig business is versatility and if you go around saying you're an organist but can't do left-hand basslines at the very least, you're not going to get jobs in jazz most likely. Most people looking for an organist want to have two musicians (bass and a chordal instrument like piano) for the price of one.
Left-hand bass lines are hard. Pedals are even harder. But when the two finally come together, and you play a solo and realize for the first time that you weren't thinking about the bass line, that it was automatic, and that you're driving the whole band... shit, there's no better feeling! I still remember the day that happened for me.
Now, if you've got something different in your head, then go for it. I have no idea if Medeski can kick bass (I'm guessing not) but that's not what he's about and he's never tried to be like that, so bully for him. It all comes down to what you want to do. But in my mind, it's better to know the instrument inside and out.