If that old synthetic oil is a few years old, it is not going to be rated SL. It might be rated SJ or even less. If your vehicle requires SL oil, use that old oil for something else. In addition, if an old sits too long on a shelf, eventually it will start to degrade, even in a sealed container. Pennzoil in an answer to a question regarding this said something to the effect that an oil can be stored in a sealed container for 18 months.
Also, if you are doing Auto-RX treatments, Frank said that conventional motor oil works best (at least when I did my Auto-RX cleaning). Unless it has changed since that time, or unless you have a vehicle that needs synthetic oil (like a Corvette), it is probably best to use a conventional oil for the cleaning.