When a new act is passed in the place of an old act, the new act shall be universally applicable and the old act is no longer can be invoked for any new companies. Even the existing companies need to follow the rules and guidelines as per the new act of 2013 and cannot claim that the new rules are not applicable to them merely because they were incorporated under the old act.
Therefore, to answer your academic question ( I am sure it is an academic question), I shall say "NO". If anybody in India wishes to incorporate a new company, they need to do so in terms of the Indian Companies Act 2013 only.
As properly opined by experts above, there is no law at all by which you would like to register your company, how can you register the company. If you want to register your company you may have register it based on the prevailing law only