Generator is defiantly not bonded as many older generators unbonded the neutral to ground bond when you switch the switch to use the 120/240 twist-loc receptacle, keep in mind that also with only a 120 volt load you are not going to get the full load from the generator as it is rated at the full 240 volt rating and with only using one side will give you only half of the generators output, the load if 120 volts will have to be split across both hots and neutral to get the full output from the generator but you can't do this with the twist-loc, we had several Colman's 5kw that had this switch and the neutral bond was lifted by the switch for using as a backup for a house, we found this out when we made a breakout box so we could have more receptacles and get the full rating of the generator from the twist loc instead of the two duplex receptacles on the generator when we checked the GFCIs in our breakout box, we just jumped the neutral to the ground in our twist-loc plug so we didn't modify the generator, I do remember some generators having a 30 amp RV receptacle that were made for RVs and if this is the case then I would expect that the neutral would be bonded? they also had the two 120 volt windings in the generator paralleled so it would produce the full output.
With the generator not running you can check for continuity between the ground and neutral at the twist-loc, or if the generator is running then using a loaded volt meter such as a wiggy or Ideal Volt-Con and check for 120 volts between a hot and EGC at the twist-loc
The test button on the GFCI should still trip which is the only UL accepted method for testing the GFCI's, GFCI's will still work without a ground if there is a path.