At first glance an argonian looks perfect for a healer, but it really isn't.

1: Restoration Expertise: Increases experience gain with the Restoration Staff Skill Line by 15%.
Re: nice for levelling but it doesn't make you a better healler. you just level the resto staff skills a bit quicker.

2: Amphibious: Increases swimming speed by 50% and when you drink a potion, you recover 6% of your Health, Magicka and Stamina
Re: the magica buff is nice, but most potions are relative expensive and has a long cooldown. the amount you recover is incredible low. You will not gain a benefit from this at all.

3: Argonian Resistance: Increases Maximum Health by 3% and Poison and Disease resistance by 23.
Re: Those are self buffs, while the core task of a healer is to heal others. This might be interesting for tanks (though they have much better racials available), but does nothing for healers.

4: Quick to Mend: Increases healing received by 6%.
re: Nice better healing....ow wait...only the healing recieved. See Argonian resistance. Just another self buff thats useless for healers.

So Argonians are not really good for healers. Actually Argonians are imo only good for role playing and nothing else.

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Onwards to the second part: does a sorcerer healer work?
First of all, all classes can be excellent healers. All you need to be a good healer is to have good magica management (e.g. through mages guild line, armor passive, food and racials) and a restoration staff.
The question is what your class has to offer for synergy.
Looking at the 4 classes, the templar has the best synergy. They have a full skillline dedicated to healing. So if you want to roll a character and want to be the best healer, there is no doubt that you should choose templar instead.
Of the other three however, the sorcerer is second best cause of the excellent magica management. But not to roll a dedicated healer.

It would more be one you would respec to be a good healer just cause your group/guild lacks decent templar healers. Or cause you happen to have a high level sorcerer and wants to be a healer for the funs.

But if rolling a new character dedicated to being a healer, I would strongly suggest the templar instead, and in no circumstance the argonian race (unless you want to be a lizzard for esthetic or roleplaying reasons)