Yeah it would be putting out full power as the battery is drawing a lot of current, but this can damage the regulators' internals too.
The battery will most likely have boiled the acid out .
Just check the Ohms coming out of the stator, it should read between 1.1 Ohms and 1.3 Ohms
Put one lead from your meter to the yellow, and other lead to the white, meter set to 200 Ohms.
The only thing i can think of if your Stator is ok and within range, is that your Regulator /Rectifier is faulty.
If it has been connected to a lighting coil, but no lights etc used, it can overheat the componants inside.
They are cheap to replace, but make sure you find one that is 12v
and if you can use a switch between the stator output and the regulator so there isn't power running through the reg/rect when the lights aren't being used.
NEW Practical 12V ATV Scooter Dune Buggy Voltage Regulator Rectifier 50 150cc | eBay
The other thing you could do instead of using a battery if you don't have electric start, is to use a Capacitor.
It will allow you to run a headlight/horn etc without a battery, but only when the bike is running.
You don't ever have to worry about the battery dying then.
You need to have the voltage a lot higher than the bikes output, so i'd recommmend a 100v 10,000uF 85c or 105c degree like these-
Capacitor Chemicon 10000 10000uF 100V Electrolytic 105C Degree 50 35 1pc FL USA | eBay
Nippon Chemi CON SMH 10000uF 100V 85°C Large CAP Snap IN Capacitor | eBay