No, you can't do this. The system pasteboard does not have any "recent pasteboard items" mechanism.
In fact, copied data is not even necessarily on the pasteboard, ever. Apps can "promise" pasteboard data by putting a type in the list of available types, but not putting any data there. An object is registered as the "owner" of that type. If some other app requests the data for that type, the owner is asked to provide it at that time. This is especially appropriate for when the pasteboard data would be expensive to produce, transmit from the source app to the pasteboard server, and stored.
So, just because you copied "foo" in an app, that doesn't mean that "foo" was ever on the pasteboard. Consequently, there's no way to go back to having "foo" on the pasteboard.
Furthermore, when something else clears the pasteboard to put new data on it, the owners of all promised data are notified so they can clean up any state they may have recorded in order to fulfill that promise. So, even the source app won't be able to provide "foo" to once "bar" has been put on the pasteboard.