The OP makes me proud. A Retribution Paladin who is asking if he can heal rather than the ones who say. "I dun heal I DPS nub." While I think you're on the right track attempting to fulfill the full role of a Paladin, I do not think it possible for a couple reasons.
1. Healing Power - Holy Paladins will be geared and talented for Intellect, Spell Crit, MP5, and Bonus Heaing. While you could match them piece for piece on gear the talents in the Holy Tree can boost Paladin healing by 35% of their total Intellect.
2. Mana Regen - Holy Paladins receive back 60% of their spell cost every time their spells crit. In a long drawn out Boss battle you would be out of mana rather quickly unless you carried an extensive amount of mana potions.
3. Mana - Right from the get go a Holy Paladin will/should have 5 points in Divine Intellect giving them an outright edge on higher base mana. A Retribution Paladin would require gems and/or enchants to boost intellect to match this, taking away more valuable slots for +Healing and MP5.
4. Bad Episode Survival - While both a Holy and Ret Paladin are difficult to kill in a PvE setting due to their bubble, there is one thing a Holy Paladin has at their disposal the Ret does not. In the event of a horribly bad link the Holy Paladin has Divine Illumination which will cut all his spell costs by half, and Divine Favor which will grant him his/her next cast an automatic crit. This enables the Holy Paladin to keep spamming their heals while the Ret would soon run out of mana and possibly lead to a party wipe.
5. Self-Reputation - While this has absolutely nothing to do with game mechanics, and could be completely disregarded, your own reputation could end up being at risk. Being a healer is a thankless job to most people, and getting blamed for things not your fault is part of the role. However, many people tend to remember their bad experiences with particular people. If something goes horribly wrong with a proper spec person, most people will complain for a short while and chalk it up to the person having a bad day and will likely invite them back at a later time albeit reluctantly. Being an improper spec trying to fulfill a role better suited for someone else could be a disaster if something goes wrong even if you are not at fault.
Like I said before the Wall 'O Text, I applaud your desire to expand beyond the role of the DPS spec but you will be most useful as DPS. That is not to say you cannot back up the healer with a cleanse or two or perhaps throw an emergency heal if a stray hit strikes your casters.
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Oxide Vanwen
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The Paragon of White Mage Excellence From Final Fantasies XI - XIV