I have a Gigabyte Z390 Arous Master motherboard, can I plug this into my LED_C1/LED_C2 ( RGB LED Strip Header ) to control the RGB lighting, or do I need to get the Corsair control module?

You need the module. They have proprietary plugs on them.

Questions & Answers: CORSAIR ML140 PRO RGB, 140mm Magnetic Levitation PWM Fan

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CORSAIR ML140 PRO RGB, 140mm Premium Magnetic Levitation RGB LED PWM Fan, CO-9050077-WW. Single Pack.

Magnetic Levitation Bearing: Dramatically reduces bearing friction by magnetically levitating the fan blade, producing lower noise and higher performance.
Dynamic RGB Lighting: Four independent ultra-bright center-mounted RGB LEDs output a vivid blast of light and color.
Expansion Kit: This product is intended as an expansion of the ML140 PRO RGB LED 2 fan kit with Lighting Node PRO. The RGB functionality of this product requires a RGB Lighting hub and Lighting Node PRO.
Complete PWM Control: Dynamically control fan speed from 400 RPM to 1,200 RPM to minimize noise or maximize airflow.
Built to Last: Long lifespan with a five-year warranty.
Replaceable Corner Caps: Customize your build with replaceable corners (sold separately).

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