Over the long term, the long term price of BTC will affect the long term hashrate.
If over the long term the price of BTC will not cover the price of electricity then miners will stop mining.
If over the long term the price of BTC exceeds the cost of electricity (to run miners) then more people will be incentivized to purchase and run miners.
The most important aspect of the BTC price is that it sets the total mining rewards - the trend of mining reward to hash rate ends up being the more interesting trend than BTC price to hash rate. Right now the total mining rewards available per day are pretty huge and so will fund a lot of mining investments (this was written a couple of months ago):
