[DennisP]

No, because transaction fees are an ongoing negotiation between miners and the people issuing transactions. That market can adjust to change in the ether price, and keep the real-world transaction cost the same. Or the fees can wildly fluctuate due to variations in traffic, even when the ether price is stable.

[lavrov]

That position isn't supported by volatile transaction fee data - excepting spikes for spam or high traffic, the transaction fee denominated in dollars generally tracks the price of ETH. Probably because the overwhelming majority of ETH activity is speculative (60% of ETH held on exchanges), and traders view transaction fees as simply a percentage of gains/losses and are more amenable to paying higher fees.