You can compost anything if you leave it long enough. My strategy has usually been to fill the compost bins, leave them over the winter, then mulch the potatoes with the contents. The first year I did this, I had to pick out loads that was still alive, and chuck it back in for another year. Year by year, the amount of stuff surviving had diminished, until it's effectively ceased. I've never had a weed re-establish itself after a season in the bins; even when I've put them out by accident, they've been too weakened to gain any strength, and have been really easy to get rid off. So just go ahead and compost them.