It depends ...
With electronic equipment in particular, delaying the effective start of the calibration interval has the potential for trouble. A number of electronic components can and do change with time -- although generally not as much in newer equipment than things did several decades ago.
Referring back to the Navy system that Hershal mentioned, here's another thing they do. If an electronic item is not going to be used for a while (maybe a month or more, but there's no hard rule) it gets a different label: "Inactive - Calibrate Before Use". The theory is that it's better to calibrate it right before it's needed. On the other hand, many physical/dimensional/mechanical tools can be calibrated and not used for a while. Generally they are sealed (for example, dipped in hot wax) so that any use of it is detectable. They have to be turned in on the due date, but if the seal is intact then it's just a paperwork exercise.
(Exception - if your'e a nuke, everything gets calibrated (with data) before and after every use!)
If I had the luxuries of time and extra available equipment, I would do an experiment. Run some random calibrations on equipment where several months have elapsed since calibration but it has not been used yet. (In a rental environment you have the advantage of exact knowledge of that interval. Many of us would have to take someone's honorable word that no, that thing hasn't been used since it was calibrated.) It may take a while to get statistically valid results, though, depending on your inventory level and usage rate. But at least you would be collecting data. Without data, all we can have are opinions.
Note that the results would have to be stratified so that you are evaluating comparable equipment - just as in interval analysis. In other words, compare spectrum analyzers and oscilloscopes separately instead of together. If you have a lot of units of the same model, break it down further by model.