No, you cannot totally eliminate the battery.
Neither the PGM nor the tacho, servo mechanism etc will work. In fact, most probably you will ruin some of the electrics letting the AC voltage from the stator pass through... this is a great possibility before the fuses eventually blow out.

I'm using a "battery eliminator" for more than two years on a mc28 bike equipped with mc21 electrics, without problems except not very good lights at idle. For 40 grams and maintenance free it's the best alternative to a battery.

I occasionally make a few and sell them on ebay but If you want to roll your own, it's a 30.000mF capacitor at 25V rating.
Just keep in mind to use a low esr computer grade capacitor and you''ll be fine. Cheaper alternatives might work but I do not know how good. Let me know if you need more details.
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