The answer is: No, you cannot. ARKit is for iOS and iPadOS only.
As you said, you can use ARCore SDK, Android SDK or ARCore Unity SDK for different platforms, but you can use ARKit only for iOS and iPadOS devices. The main reason, why you cannot use ARKit for Android devices is IMU sensors (gyroscope, accelerometer, magnetometer, etc): all Android devices need a thorough sensor Fusion calibration in order to observe the same AR experience. All Apple devices (A9 to A14 chipsets) have almost the same sensors (iPhones SE/6s/7/8/X/Xs/Xr/11/12) and these sensors were similarly calibrated.
Nevertheless, if you want to create Android AR app in Unity using ARCore, it's easy. For that you need Unity, Vuforia SDK 9.5 (you can install it with Unity or download an importable package from Vuforia website) and Android SDK.
Vuforia uses ARCore/ARKit technology if the hardware it's running on supports it, otherwise it uses its own AR technology and engine as a software solution without dependant hardware.