I think there's a lot more to picking sticks than picks (and I've done both over the years). Picks come in thicknesses, textures, etc. but they all fit in your fingers essentially the same and have very similar action. Sticks come in an incredible amount of variety, with different playing actions and sounds depending on length, tip, taper, weight, material, diameter, etc. etc. etc.
I guess if you have an uncomfortable pick, it can affect your playing, but I know that if I grab a pair of sticks that are not correctly sized, and try to play for a couple hours, I can get the claw hands.
All the time, guitarists lend each other picks. I carry my stick bag when I have a reasonable expectation of playing when I go somewhere.
So no, don't pick sticks the same way as picks. You need to make sure they fit correctly in your hands, have the proper amount of rebound and control, and are straight and true. A lot more care needs to go into choosing sticks, in my opinion.