No-till drills are super expensive and they don't like hitting hard objects. A lot of pressure is put on those openers to enable them to do no-till seeding effectively, and hitting something hard that doesn't have a lot of give will break disks and can bend and twist the openers. The openers are designed to penetrate soil and stubble, so they might penetrate some of the wood chips, but I don't think they would do it consistently enough to justify using a drill. I think it would push and tend to clog a lot more than you'd want it do. With a no-till drill, the drill is generally running over stuff that is still anchored to the ground by a root system, and is long and thing. Corn and milo stubble get a little thick, but they are probably easier to cut through than wood. I've not every tried to run a drill behind a mulcher, but mulching isn't that popular here so I don't have a lot of experience with it. Everything here is generally grubbed and raked before a drill is run over it.
I would hate to burn the mulch because of the shading and moisture retention benefits. I'm wondering if maybe you could use seeds that can perhaps just be spread? What are you trying to plant?