Can druids solo-heal heroics?
Absolutely, without a doubt. As a shadowpriest in the single-player game, my usual daily heroic group has a druid as the healer.

How is the survivability of druids vs paladins when I may not be able to give them my full attention. Is throwing an instant HoT and shifting into bear as effective as a paladin standing there with a shield?
They're different. A druid performs better while mobile, and a paladin performs better while taking hits. A druid likes consistent incoming damage, and a paladin often heals reactively. A druid is flexible in terms of what role it can play in the same fight, and a paladin offers more group enhancements and buffs. With that said, in your example, no, a druid throwing a hot and shifting will not be as effective as a paladin simply because the druid stops healing whereas the paladin doesn't. Of course, most pvp druids won't just sit in bear form after tossing a heal, they'll try and run, healing on the move.

Will the Heal-over-times be worth the loss of blessings?
Hot's are the primary way druids heal, they're not a bonus. Contrawise, blessings are just one of a paladin's strengths. If you want to make a comparison, look at *all* of their advantages and disadvantages. In the end, you should decide which fits the way you like to multi-box.

As a final note, I will caution you on pve with a single druid as your healer: the battle-res timer is very long, and it's your only means of resuscitation. This issue goes away if you run with shadowpriests or paladin tanks, but keep it in mind for the group you have now.