Again, a relative argument. It would be wise to realise that an executive chef normally, even if employed, runs his/her own kitchen. It is their domain, and it is vital that they are aware of the loopholes involved in running it.
To help you understand a bit better. You have 2 chefs working at the same restaurant.
One has his culinary ed sorted out, the other has both culinary and a management course (not necessarily a degree, just any certification).
Both chefs are very good, and are working their way up in the kitchen hiearchy.
A time comes, when these 2, almost equally matched chefs are both considered for a promotion to the exec level.
Any employer, taking into consideration both factors, would notice the following:
Both are good chefs.
Only one has proven and documented managerial skills (his degree)
It would only be rational to pick the more qualified one.
It is just a perspective.
Some advice, if you will.
You have the freedom of choice... Use it!
It all boils down to what you are more comfortable with.
Consider a 2 year Diploma in hospitality management, on a Part time basis.
Once you have completed your culinary certificate, jump into the job market, start cranking up those experience points! At the same time, while you build your hands on aspects, sit the part time program.
2 years later, you will have both (assuming you pass and graduate) a fancy and, may I add, Credible piece of paper, as well as a decent exposure to the line of work.
The management aspects also open a lot of doors, outside the kitchen.
If you should ever get tired of cooking, and wish to delve further into the industry, the management course will grant you the skills and attributes needed to enter an ownership class, where you can run your own establishments etc.
It certainly is something I consider to be very useful.