DIAGNOSIS Absolutely. The electric start is just a convenience feature. The engine itself is fully pull-start capable, designed to work even with a completely dead or missing battery.
FIX First, make sure the engine switch is in the ON position. Locate the pull cord handle. For a cold start, move the choke lever all the way to the CLOSED position. Pull the starter cord slowly until you feel resistance (this is the compression stroke), then give it a brisk, full pull. Don't yank it erratically. It may take a few pulls. Once the engine sputters to life, gradually move the choke lever to the OPEN position over the next 30 seconds as it warms up.
IF THAT DIDN'T WORK If it's unusually hard to pull or won't start, don't force it. Check the usual suspects: Is there fresh fuel? Is the oil level correct? Is the fuel valve ON? A dead battery shouldn't affect these basics.
HEADS UP Even when using pull start, a completely dead battery can prevent the inverter from producing power. The inverter electronics need a small amount of 12V power from the battery to "wake up." So you might get the engine running but still have no AC output. You'll need to charge or replace the battery to get power, even though the engine runs.