It looks like the AMA says no. Here is an excerpt (emphasis added):
When time is being used to select the appropriate level of a service for which time-based reporting of shared or split visits is allowed, the time personally spent by the physician and or other qualified health care professional(s) assessing and managing the patient
on the date of the encounter is summed to define total time. Only distinct time should be summed for shared or split visits (ie, when two or more individuals jointly meet with or discuss the patient, only the time of one individual should be counted).
When prolonged time occurs, the appropriate add-on code may be reported. The appropriate time should be documented in the medical record when it is used as the basis for code selection.
▪Total time
on the date of the encounter (office or other outpatient services [99202-99205, 99212-99215]): For coding purposes, time for these services is the total time on the date of the encounter. It includes both the face-to-face and non-face-to-face time personally spent by the physician and/or other qualified health care professional(s) on the day of the encounter (includes time in activities that require the physician or other qualified health care professional and does not include time in activities normally performed by clinical staff).
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You can bill the non f-t-f time from another day though:
Codes 99358 and 99359 are used when a prolonged service is provided that is neither face-to-face time in the outpatient, inpatient, or observation setting, nor additional unit/floor time in the hospital or nursing facility setting. Codes 99358, 99359 may be used during the same session of an evaluation and management service, except office or other outpatient services (99202, 99203, 99204, 99205, 99211, 99212, 99213, 99214, 99215). For prolonged time without direct patient contact on the date of office or other outpatient services, use 99XXX. Codes 99358, 99359 may also be used for prolonged services on a date other than the date of a face-to face encounter.
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Personally, I think it's an oversight. Right now, you can include work from a different day when choosing the E&M level, and without a statement saying that is no longer true, it would seem to me to be that it were still true, hence the oversight.