Illustrator does not need a Graphics card to run so it will continue to run even when you have a graphics that is not compatible. It is just the GPU will be disabled.
Intel HD 4000 is an old Graphics perhaps 5-year-old. you can see recommended graphics here on our system requirement page: https://helpx.adobe.com/in/illustrator/system-requirements.html
I have an HD 4000 in both my Macbook Pro and my Dell 15R. Both are OpenGL 4.1/1536 MB vram and are active in the Preferences > Graphics options.
So Yes and No. It can deliver graphic enhancements, but may be choppy for anything intensive. Worth a try.