millions upon millions of home GAS powered standby generators run their weekly or monthly exercises WITHOUT ANY LOAD on the alternators. it is the commercial units, like hospitals, that are required to run loaded tests.
diesels have issues with running low or no loaded testing, as they dont build up any heat running so slow.. wet stacking. its caused by running long periods lightly loaded. the engines dont use spark plugs so the cooler running temps lead to incomplete combustion.
I usually recommend to my clients to manually power off house at least once a year for 30+ minutes and run house load under generator. Preferably before winter. this is mostly to make sure everything is powering up and running ok prior to winter months.
Otherwise the generator will run for 5-12 minutes (depends on generator model) and WILL NOT TRANSFER THE LOAD, every week , bimonthly or monthly.