Well, I finally got myself the original Sharp CE-BC21 external charging unit AND the EA-70 AC Adapter, with a EA-BL08 spare battery (no half measures taken )
Here's my full story...
Having the EA-BL08 in the (slightly
modified) external adapter, I connected the AC adapter to my C750, to see if it would charge my "old" EA-BL06 in the unit.
After 5 minutes the charge LED began flashing again, just like before, which gave me the impression that the charging circuit had a defect somehow. Therefore, I placed the larger EA-BL08 battery, and charged the smaller EA-BL06 with the external charger.
The Zaurus booted, and everything worked fine,
including reading of CF-cards. Lucky me
Now, here's the strange part. After completely charging the EA-BL06, I placed it in the Zaurus. Guess what, since then, charging the battery also works with the AC Adapter... no flickering charge LED anymore, all works perfect
I don't know, I guess my Zaurus was waiting for eh... the mood to be right??
Anyhow, I removed the battery, and connected the AC Adapter while pressing D+B. The Zaurus boots, I login, enter superuser mode, and type ./sbin/reboot. This reboots the machine, and in my case starts Cacko 1.20.
This all without having a battery in the machine! After rebooring, all works fine, except for reading CF-cards, they simply aren't recognized. This unlike SD-cards which can be (un)mounted without trouble. As a matter of fact, mounting a CF-card results in the Zaurus being shut down completely.
So, to give an answer to my own question, yes, I guess the Zaurus needs battery power for using CF-cards.