The cost of executing a smart contract is measured in Gas. The units of Gas consumed during an execution is paid for using ether by multiplying units consumed with
GAS_PRICE is set in the transaction.
Suppose an execution costed 1000 units of GAS and the account that submitted the transaction had set 1 Wei as the
GAS_PRICE, then the total cost of Execution is 1000 Wei. Assuming
GAS_PRICE is constant, the total cost in ether will be constant. This means that if the cost of ether in terms of a fiat currency is increasing then the cost of execution in terms of that currency is also increasing.
GAS_PRICE is in reality not a constant and is market determined(demand-supply). Since we are assuming that Ether Price is going up, I also assume that the demand for submitting transactions is also moving up. In that case
GAS_PRICE can go down only as a result of large number of miners who are ready to mine at cheaper
GAS_PRICE joining the network. This is not a possible scenario.
Since Ethereum is a non discriminatory network with the vision of universality, there is no argument of regulating gas price. So I guess in short, if Ethereum price with respect to a currency is going up, it will be costly in that currency to execute transactions in Ethereum.
You can read more about Gas here