Yes. Just like the proven SRAM RED and Force eTap AXS rear derailleurs, the spring clutch equipped Rival eTap AXS rear derailleur is capable of excellent 1x chain system management when paired with the Rival 1x crankset’s narrow-wide chainring tooth profile.
The Rival eTap AXS rear derailleur will work with AXS 12-speed cassettes from 10-28T up to 10-36T. Additionally, using an Eagle AXS rear derailleur, Eagle AXS 10-50T or 10-52T cassette with an Eagle 12-speed chain with Rival eTap AXS controls and 1x crankset is also possible.
See the AXS Components Compatibility Map in the "Compatibility Map" section of the SRAM Service Site to learn more.