Running a generator without the battery connected is not a good idea - - - - -the battery acts a a sort of "shock absorber" and dampens out high voltage spikes. If the engine will run with the battery disconnected, the generator has at least some output, however. Against a fully-charged battery, a 6 Volt generator should be regulated at approximately 7.5 volts. A 12 volt unit should reach about 14.5 volts before the regulator kicks in. When it's charging a low battery, the generator won't reach those maximums because the battery will accept a charge at a lower voltage. Measuring the voltage at the battery posts is as good a way as any to check for generator output. If the engine-running battery terminal voltage is at, or below the terminal voltage with the engine stopped, and does not rise when the engine is at fast idle, the generator, regulator, or both are likely to have problems.
Jerry