Yes, the little alternator is just supposed to maintain the charge in a healthy battery, not recharge it. You need the 10 Amp one to charge a battery. However once you have everything running properly, and the battery charged, the system you have should maintain your battery, and allow it a long life. It is best to use a battery charger to deal with a flat battery - the number of hours your alternator would take to recharge it would be ridiculous.
I look forward to hearing from you when you've gone through the carburetor tuning procedure, and also checked that there is at least a little current going into your battery. Please be sure your engine is full of clean oil - the Synchrobalance system it has in its crankcase is very unforgiving of poor lubrication.
