Hi & welcome! Sedum roots reliably without any roots at all, so taking root shouldn't be a problem. Are you able to show a pic of one of the plants you got? I don't think I've heard Sedums referred to as "bare root" before.
But few plants would enjoy baking on black plastic.
I also fear the roots of the weeds under it aren't dead (bindweed isn't that easy to kill, a smothering could take a year or more, and tilling increases the number of plants because it can grow from pieces of root.) If bindweed has dropped seeds in the past, which it does copiously, surely some will be near holes that have been poked.
I would strongly encourage you to replace the plastic with corrugated cardboard, overlapping the seams very generously, then covering that with at least 6" of organic matter* to completely block the light and provide enough weight so that growth can't occur under it. This will not need to be removed later, will add tilth and fertility to soil, and help moderate soil temps and moisture levels, as well as cultivating a healthy crop of soil microbes and other soil dwellers like earth worms. Leaving it undisturbed except for the holes you'll eventually dig to add plants later will also prevent whatever seeds that have fallen in the area over the years from being able to sprout (except those few that get shifted to the surface while you're adding plants.)
Is your Sedum 'Red Dragon?' If so, it's a ground cover/low creeper, it should be able to take off right on the surface of the smother, as long as the top layer isn't too chunky/bumpy.
Organic matter = compost (already fairly decomposed organic matter) &/or anything that can decompose, like mulch, leaves, pine straw, coffee grounds, kitchen scraps, poo, grass from mower bag (you'd want to mow before grass is showing seed heads if doing that,) small yard trimmings, shredded paper or bark, etc... the more of a mix, the better, vs. just inches of 1 thing.
