Will reseeding plants like spider flower (Cleome), Verbena bonariensis, cosmos, and others successfully seed themselves through 2 inches of mulch applied last fall?

Well… yes and no. The three annuals (and might I add, prolific reseeders) that you mentioned are sure to show up again in your garden, however, not necessarily where you wanted them. They won’t actually start sprouting with a good cover of mulch. Assuming that you had mulched with a shredded wood material, the myriad of seedlings cast upon the wind will most likely end up in the cracks of your (and possibly your neighbors) flagstone, and practically any spot where it can reach the bare soil. All three of these annuals can easily be lifted and relocated back into your garden. Then next fall, if you clear a patch of mulch from the soil and shake a few dried seed heads over the soil in the desired garden bed, you’ll more than likely get at least a few in the “right” spot.