I'm not versed on specific water usage by rice paddies but am aware that:
The inland Central Valley of California was historically a seasonal or episodic lake. The Great Flood of 1862 saw 3m (10 ft) of water dumped on the state over 43 days from December 1861 through January 1862, followed by a warm storm melting much of the snowpack:
The entire Sacramento and San Joaquin valleys were inundated. An area about 300 miles (480 km) long, averaging 20 miles (32 km) in width,[21] and covering 5,000 to 6,000 square miles (13,000 to 16,000 km2) was under water.[15] The water flooding the Central Valley reached depths up to 30 feet (9.1 m), completely submerging telegraph poles that had just been installed between San Francisco and New York. Transportation, mail, and communications across the state were disrupted for a month.[22] Water covered portions of the valley from December 1861, through the spring, and into the summer of 1862.[15]
https://en.wikipedia.org/wiki/Great_Flood_of_1862
Much of the valley still floods seasonally, with designated flood zones such as the Yolo Bypass, between Sacramento and Davis.
A key problem within the central valley has been groundwater loss resulting in subsidence exceeding 15 m (50 feet) in places. Flooded paddies might help contribute to groundwater recharge.
Much of the paddy water is through-flow, which I'd presume returns to river flows. What the impacts of ag practices (fertiliser, pesticides) are I'm not sure. There will also be evaporative losses, of course.
I'd like to see a net impact / net flows analysis. The picture's likely more complex than a brief glance from the highway would afford, however.