Does OnApplicationQuit() get called on non-monobehaviour objects?

Curious as to if onApplicationQuit() would be called on a regular class that is

using UnityEngine;

Example:

using System;
using UnityEngine;

public class Foo
{
    void OnApplicationQuit()
    {
        Debug.Log("Application Quit");
    }
}

Then

using System;
using UnityEngine;

public class Bar : MonoBehaviour
{
    Foo = new Foo();
}

Would Foo->OnApplicationQuit() be invoked?

No, all the On* functions are part of the MonoBehaviour class only.

No. The class have to be Monobehavior.
There is no Update(), Start(), OnEnable(), and the other function. Read it: