The simple answer is no, it's not possible. Based on ESRI tech support response,
"While you can cache a time-aware service, the time-aware functionality will be lost and the data will just display at one time interval. So essentially, it doesn't work....I've logged a documentation bug for this, since it is not explicitly stated anywhere..There is also an existing bug...It's an enhancement request to add a warning that tells you when you switch to a cached map service that you will lose time-aware functionality."