I haven’t ever had double tulips come back a second year, though some of my single ones have. Some varieties are more likely to perennialize than others. Another possible problem is that voles and other plant eating critters find tulips scrumptious, so they are more likely to be eaten than other less palatable bulbs like daffodils or alliums.

I think it's worth a try. Just clip the flower stem after it fades and just leave the foliage as long as you can stand looking at it. I've had the early double tulips come back for a couple years but the later ones have been more of a gamble.