Out-of-date solder wick can create a performance issue. As more oxidation builds on the copper braid, it will take longer to activate and draw up solder. It will slow down a little month-to-month until eventually the performance will be unacceptable. We estimate this to be 2-years based on average storage conditions. Wick in storage wrapped up tight can last longer, while a loose bobbin sitting on a benchtop will probably go bad sooner.
An operator will generally have a feel for how wick performs and will have an opinion on when performance is unacceptable. The main risk of using out-of-date wick is thermally stressing the working area, adjacent components, etc. When an operator tries to make due with old wick that is underperforming, they tend to turn up the heat on their iron, or keep the tip in contact with the wick and work for a longer period of time.
So whether or not out-of-date wick is considered good depends on the criticality and conservativeness of your process. An average shop would keep using it until it stops working well. A very conservative process (e.g. for class 3 electronics) could require wick in stock to be discarded at the expiration date, and loose bobbins at workstations replaced periodically (i.e. weekly or monthly).