Last time I was there, no. Apparently they did when they opened, but stopped because it was too much of a hassle. If it's not on their website menu they're still not serving them.
They do not serve milkshakes.
I was just there a few days ago. They don't serve milkshakes. They have soda and "fizzy drinks", which are just soda water with fruit in them.
Thanks! Your answer is awaiting moderation.