If you're already a good healer and (key) haven't learned to rely on the Holy talents, you can heal as shadow in decent gear. I've healed all of Shadow Labs, Botanica, Steamvaults, and Shattered Halls, though I admit the PuG's I end up with tend to be pretty good. Also, I make sure the group has someone who can backup heal in case I run oom - I prefer a druid, for Innervate, but as long as there's someone you should be okay. Lots of CC helps too.
Whether you're holy/disc, disc/holy, or shadow, you will need a pure +healing set. It's just not possible to heal without it once you get into level 70 instances. I'm running +1k healing, almost 400 spirit, and 40 mana/5 in my healing gear atm, and not a single piece of my healing gear is the same as my damage gear.
That said, provided you've got some decent gear, you should be able to get groups as playing DPS. A shadow priest, a warlock, and a pally are an excellent combination.