Almost every Subway I've seen is packed during the lunch hour, sometimes with lines forming outside the door. With so much demand for its sandwiches, vegan options will receive a lot of visibility and maybe some new customers. If consumers like the products then it may influence menu options at other fast food chains as well which is good news!
I don't have any statistics on what percentage of meat production is absorbed by fast food restaurants; if the percentage is large and if vegan options grow in popularity at fast food chains, it could eventually reduce demand for animal agriculture. It will be interesting to watch how Subway's move impacts the industry and consumer eating habits in the future.