CG Employer never adopted the plan, but participated

Controlled group with 4 companies.  Only 3 of them adopted the plan, but all four companies are participating.

Can we do a retroactive amendment having the missing company adopt the plan back to 2013?

Yes, you can generally adopt a retroactive amendment to the plan to reflect its actual operation (in this case, inclusion of the 4th company in the plan). As I recall, it would have to be done under VCP. This is not SCP eligible. 

Check the plan document.  Most, but not all, plan documents require that an employer affirmatively becomes a participating employer before its employees become eligible.  However, there are some plans where employees of an employer that is in the same controlled group as the adopting employer become eligible without any further action.

If you find that the employer needed to affirmatively become a participating employer, than Former Esq. answered your question correctly:  your client will need to make a VCP submission, not a self-correction.