no, they probably won't. The factories usually have only several set up for powered usage while on the generator, or on the inverter(if you have one). The generator may not have the same output as your 30a or 50a Shore Power cord connection, so limiting the number of outlets is akin to saying that the generator is not designed for numerous connections.
usually a residential fridge is the first concern, then a TV outlet, and maybe one other for general purpose usage.
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