Can it? Of course. N/G bonding is a different question- most people remove any bond in the generator and use the existing bond in the house. (Depends on a lot of missing info, like whether there's a transfer switch involved.)
Is this generator being set up as an SDS? If so doesn't connecting it to the house GES defeat the purpose of switching the neutral? The generator GEC goes to the house GES which has a GEC directly back to the neutral of the house panel.