This is a very interesting question which can unfortunately be answered with a simple word... something that in our case would be "no". Sure, you had lots of references and throwbacks to supposed Roman values and symbols - even to the Empire of old - but in the end it was all just plain propaganda, and should therefore be taken as such.

Also, don't forget that the Empire which was proclaimed in 1936 was in fact an Italian one (the purported successor to that of the Romans) and that a kingdom - the Kingdom of Italy - laid at its heart, whose monarch (Victor Emmanuel III) would have probably vetoed such a proposal should one have ever been advanced.