Nope, I'm not convinced yet it is a battery, and cannot find reference to such anywhere. Probably a capacitor that has enough juice to maintain the clock between battery exchanges. But I have another idea to test this. Stay tuned.
OK - here's the deal. I have two 1s; one essentially new (<500 shutters; backup for when my main one dies), and another which I use (main one). New camera had juice in battery and correct time (from last year); main one was dead from more recent last use. Put fresh recharged batteries in each. Set time in each (only the main one asked for it). Then took out batteries for 8 minutes and replaced. Main one maintained correct time. New camera did not. Then took out batteries for 1 minute and replaced. Both cameras maintained correct time. Then took batteries out for 2 minutes and replaced. Main camera maintained correct time, new camera did not. Then took batteries out of new camera for 90 seconds and replaced. New camera maintained correct time. Waited an hour. Took new batteries out of new camera for 2 minutes and replaced. New camera now maintains correct time.
Conclusion: I think it is a capacitor, one which has enough juice to power the clock during a battery change (minutes), not a battery charge (3+ hours). As indicated by 2 minute retest, duration of capacitor charge increases the longer a new battery is in it. However, much longer duration of capacitor charge in older camera (8+ minutes, with initially long dead battery), suggests something else going on. Newer camera has similar, but later serial number (by about 5000). Perhaps Olympus changed capacitor specs in mid production run (if that's what it is, and in any case, not described in manual, assumed deep inside the assembled camera), and it varies.
In any case, I always keep two+ extra batteries with me and check the charge before I go out to film (do we use that word anymore?), so honestly, I've never noticed this clock issue.