I think it does and here's why: If you can make a bitcoin for 1$, why would you buy one for 300$? It does influence the price, but it's not the only factor determining it's price.
Good point, I was kicking around the idea that btc was base pricing itself to the aggregate cost of mining, and now someone else confirms my suspicion..thanks.
Sorry. It is not a good point, because it assumes that the entire demand for bitcoins could be satisfied by mining. In fact, the number of bitcoins obtained by mining would not change, so the number of bitcoins traded on exchanges would not change.
For example, let's suppose that 1000 people want 1 bitcoin each, 100 bitcoins are mined, and the price is 300$. 100 people would get mined bitcoins and 900 people would buy the bitcoins for 300$. Now, suppose the cost of mining bitcoins drops to 1$. Still, 100 people would get mined bitcoins, and 900 people would buy the bitcoins for 300$ each. Nothing has changed.
Furthermore, if it only costs 1$ to mine a bitcoin, then people would start mining like crazy and the difficulty would rise until the cost of mining a bitcoin is about 300$. The price of a bitcoin determines the cost of mining.