Coolant pipe

No, that isn't just overflow, it is a purge line to keep air out of the cooling system. You will need to replace that line to keep the engine happy and prevent cooling system problems.
Be careful though as Audi plastic tends to get very brittle with age. While you have the system drained it might be a good idea to replace any other suspect plastic as well.

Thanks for your response, Steve. Now I have another problem. I replaced the serpentine belt yesterday, drove fine all day then when I started it last night the belt popped off and continues to pop off every time I start it, what could cause this?

Look at the belt routing to see if maybe a clamp or piece of the broken tube got stuck in a pulley or tensioner. If the broken part leaked coolant it could contaminate a bearing causing problems. Was the belt change the reason for the broken part?