Funk works great with a pick, the muting, pinch harmonics, chording, stroke variation etc all lend itself to funk.
I set up a bass recently for funk, what I look for is a slight 'buzz' in the frets on and above the 12 fret.
So the action is kinda low, but more important is the fact a take a bit of relief out of the neck....so it does not have forward relief to clear those frets, it actually buzzes them.
But below the 12th fret, and as you close in on the nut, from the 7th fret down it is hardly audible unless you 'dig in'.
Some video was shot of how and why I done it, the footage gives an insight into how the set-up adds to the sound and feel of not only what I was after, but the effects used with it....and of course the effects that can be gained from the expression of the player and the instrument.
If I can get a hold of it I will post a link to it, some of the pick stuff was cool.