No, the 20 amp rated cord does not have the same configuration as the the 30 amp outlet on the generator. It will not physically fit. You can use the adapter, but keep in mind that the generator's breaker protection is for 30 amps, but the wire of the cord is only rated for 20. Therefore, under heavy load, your cord will get hot, and ultimately may heat stress the conductors, further damaging them. Just play it safe and buy a heavier gauge cord. I know they can be expensive, but if you order them online, from sites like Amazon, they can be much cheaper.