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>will it spider through the site at all since the mainpage is nothing but a redirect
Probably not. It will find the old domain as the relevant one since it contains all the content.
>Company does not want me submitting anything referencing the old domain name?
I would put all the old content under the new domain and redirect the old domain to the new one. That way the SE'S will index the pages under the new domain. I would use a 301 permanently moved redirect.