If I upgrade to a SRAM Eagle chainring, do I need to use a SRAM Eagle chain?

No. The X-SYNC 2 chainrings are also compatible with our SRAM 11-speed components.

Note: If using the X-SYNC 2 chainring with an SRAM 11-speed drivetrain, then you should use an SRAM 11-speed chain. If you are using an SRAM Eagle drivetrain, you must use an SRAM Eagle chain.