Bitcoins have most certainly gone up in price due to GPU mining and lack of energy efficiency. The more energy put into the system, the more coins cost to make, the higher the bitcoin price is.
No. The causal chain is Market => Price => Total mining reward => Incentive to mine => Amount of miners => Difficulty => Cost to mine. The other direction, the direct influence of the specifics of mining on the coin price, is negligible. If cost per hash was lower, there would simply be more hashes and larger difficulty thus maintaining market equilibrium. (though there are indirect effects due to network security, popularity etc).