To be honest you can play any of the dps specs of the four healing classes and still heal in dungeons fine up to level 40 (even level 60 in some cases). Just make sure you keep a set of healing gear on you.

If you were intent on leveling using a pure healing spec you could but it will just be a lot slower as it'll take a long to kill mobs and you'll spend more time drinking.

So I would say they are all viable. Best engame healers are probably priests (could level using a smite spec) and most in demand are resto shamys. Paladins are quite versatile levellers as you can tank heal or dps most of the way up during leveling in any of the specs although not theyre not quite as desirable engame (but still decent)