Assuming it’s connected before you paint it, no. Paint away!

You don’t want to paint first in case your paint is a poor conductor.

If the paint is latex, that's not a great conductor.

Paint will not impact the function of the braid. However, you would not want to get any paint near the contact points of the braid and the other metallic items that the braid is electrically connecting to ground. It is possible that if this were to occur, the paint could act as an isolator and prevent the braid from being in electrical contact with other metallic components.

Given that the braid seems to be installed after any painting, from an aesthetic standpoint it may be a good idea to not paint the braid as this is not customarily done though there is no harm as long as the above guidelines are followed, it just may not look “right”. Hope that helps!

If you want to look really slick cover it with colored wire braid sleeving.

Painting it unless it's a contrasting color to the cabinet just seems like a not-great way to have it blend in. What I'd probably do if I cared about the way the insides of my cabinets looked (I don't, yet.... but I think my future plans will include stuff like this) is sleeve it in clear tubing, so it's protected and you can see the shiny silvery goodness standing stark out from the color of the cabinet.