Copetown, the purpose of ice bath chilling is to rapidly and thoroughly reduce food temperatures below the Food Danger Zone. As long as the sausages are completly cooked they should be safe with refrigerated cooling because they are realtively thin as compared to other meats.
The generally accepted standard is to have potentially hazzardous foods' temperatures in the Danger Zone for a cumulative time of no greater than 4 hours. That length of time includes all pre- and post-cooking times.
Food processers are required to monitor and record those times and temperatures as proof of safe food. At home you just want to cultivate a general awareness of the time and temperature foods that are in the danger zone.
Achieving Pasteurization would be better if the sausages are destined for lengthy cold storage which i define as beyond 72 hours after cooking.