Hi, default odoo doesn't give option to import invoice status. So while we import invoices, it will be in draft state. You have to enable the field "State" in import option to import invoice status by code customization. Please refer the following 

    state = fields.Selection([

            ('draft','Draft'),

            ('proforma', 'Pro-forma'),

            ('proforma2', 'Pro-forma'),

            ('open', 'Open'),

            ('paid', 'Paid'),

            ('cancel', 'Cancelled'),

        ], string='Status', index=True, readonly=False, default='draft',

        track_visibility='onchange', copy=False,

        help=" * The 'Draft' status is used when a user is encoding a new and unconfirmed Invoice.\n"

             " * The 'Pro-forma' status is used when the invoice does not have an invoice number.\n"

             " * The 'Open' status is used when user creates invoice, an invoice number is generated. It stays in the open status till the user pays the invoice.\n"

             " * The 'Paid' status is set automatically when the invoice is paid. Its related journal entries may or may not be reconciled.\n"

             " * The 'Cancelled' status is used when user cancel invoice.")

Hope this help you,

Thanks & Regards.