If you define HFTs as passive spread/rebate-capturing single instrument market-makers, then yes, but many prop HFTs operate a "hybrid" model where they sometime

If you define HFTs as passive spread/rebate-capturing single instrument market-makers, then yes, but many prop HFTs operate a "hybrid" model where they sometimes cross the spread to flatten their book, or cross if an arbitrage presents itself. There are even HFT strategies that are primarily liquidity taking.