Taken from the Morrowind Battlemage class description, Morrowind Battlemages were lacking the restoration skill, as did they in Oblivion.

I've logged 384 hours on Skyrim and I've yet to create a single potion. I'm re-rolling my freshly created Battlemage and I'm interested in exploring alchemy as a minor skill. I only use restoration for healing (haven't tried the new Dawnguard spells though), I seldom or never use wards. Would it be efficient to replace restoration altogether with alchemy?
I haven't got a clue about how it would work out but I'd use it to create healing/stamina/magicka potions and utility potions like invisibility and fear poisons. Would I gimp myself by not using restoration as well (bar the base healing spell). I don't plan on making this character a vampire so I don't think I'll miss necromage that much, though I'm a bit unsure about Recovery and Respite.

I never felt much use for the Restoration skill, as potions are quite abundant in the game as it is. With Alchemy added to the mix, you should rarely run out of health potions. The addition of other potions and poisons, in my opinion, makes Alchemy a better skill.