This has now changed as of summer 2021, but only if you're truly driving straight through by the most direct route without any stops at all. According to the FAQ:
Do I need a day-use reservation if I am just driving through the park?
You can drive through the park to reach a destination on the other side of the park without a reservation. The entrance station ranger will provide a time-stamped permit valid for the time needed to travel from entrance to entrance. You must drive the most direct route to exit the park; stopping is prohibited. Violating park regulations can result in a fine of up to $5,000 and/or six months in jail.
The park entrance fee still applies and provides access to visit Hetch Hetchy during open hours when it's not full.