Can a custom View know that onPause has been called?

Yes you can using below code,

@Override
protected void onVisibilityChanged(@NonNull View changedView, int visibility) {
    super.onVisibilityChanged(changedView, visibility);
    if (visibility == View.VISIBLE) //onResume called
    else // onPause() called
}

@Override
public void onWindowFocusChanged(boolean hasWindowFocus) {
    super.onWindowFocusChanged(hasWindowFocus);
    if (hasWindowFocus) //onresume() called
    else // onPause() called
}

@Override
    protected void onDetachedFromWindow() {
        super.onDetachedFromWindow();
        // onDestroy() called
}

@Override
    protected void onAttachedToWindow() {
        super.onAttachedToWindow();
        // onCreate() called
}