The answer is: no!
Putting ice on a sprained ankle creates vasoconstriction, slows down blood circulation, and increases swelling. Why do we have swelling? It is an accumulation of fluid produced during the inflammatory phase of an injury that aims to clean an injured area of the blood accumulated from the torn ligament. This cleaning phase, which can be compared somewhat to the demolition phase during a renovation project, produces liquid that is trapped in the lymphatic vessels. It is for this reason that wearing a pressure bandage is a better idea as it helps to mobilize the swelling during the inflammatory phase.
There are three healing stages: inflammation, vascularization and proliferation. How can you speed the healing process? With movement. For example, if you suffer from a sprained ankle, pedaling on a spinning bike will favor muscle contractions around the injured tissues which gets the fluid accumulation from the lymphatic and venous systems to circulate. This action also stimulates the blood, which is rich in oxygen and nutrients, to flow towards the injured area and promotes the excretion of carbon dioxide and metabolic waste.