Storing potato water: how long can it be refrigerated?
Yes, shelf life would be similar to homemade stock. It has the same potential for cross-contamination, and natural contamination (with a slightly reduced chance for contaminates from ingredients, as there is no meat).

Be sure to cool and refrigerate quickly (cool pot in a sink of ice + cold water). If left to sit out, warm + starchy water is a great breeding ground for un-fun microbial life.