Short answer: yes
Long answer: since 1inch runs on the Ethereum blockchain, its operation is compliant with the network’s inherent rules and design solutions. One of them is proof-of-work (POW), the basic consensus algorithm used to verify transactions and produce new blocks on Ethereum. This work is done by miners, and, as any other job, it has to be paid. Here is when ETH comes into play, as it incentivizes miners to verify transactions. Gas fees you are charged each time you transfer funds across the network are rewards that miners receive for processing your transaction. These rewards are paid in ETH. Plus, miners get rewarded by small amounts of newly minted ETH.
Therefore, to trade on 1inch, you need a sufficient amount of ETH to cover the gas cost of a transaction, which, in turn, can vary based on the transaction size of the specific assets you trade.
More about mining here.