An animal such as a crayfish relies on gravity to keep its circulatory system running. If it is turned upside down, the gravity works against the system, suffocating the animal. Now if, instead of placing the animal on it's back, we were to take take it to a space station, gravity would not be working against it, and random blood flow plus capillary action should get some blood flowing. Would the animal survive this?
I believe that fruit flies have been taken aboard the Space Shuttle for experiments. They survived and the adults have an open circulatory system.