LEED, an acronym for Leadership in Energy and Environmental Design, is a trademarked title owned by the US Green Building Council. When the owner says that they are "implementing the LEED program," alarm bells go off in my head. The alarms have to do with trademark infringement.
In order to become a "LEED Certified" building, the owner must first register the project with the USGBC. That requires submission of a large fee. Then the project must be carried out in accordance with their design standards. There are certain things that every project must have (a recycling center is one), and you can get points for including certain features in the design. If you get enough points, then your project will be awarded status as LEED Platinum, Silver, Gold, or Certified, depending on the total number of points.
However, in order to be formally credited with any specific point, the owner must submit to the USGBC a specific set of documents that prove that the project did indeed incorporate the required design features required for that specific point. It is no easy task, and it is not a cheap task either. The total volume of paper that must be submitted to achieve LEED Certification would fill up a large bookcase.
So, again, when the owner says they are implementing LEED, I have to wonder if that means they have committed the money and other resources necessary to carry out the process. Many times, an owner wants to have the word "LEED" tied to the project, but is unwilling to spend the money to get it legally, or is just unaware that there is a process that must be followed in order to earn the right to use that word.
To answer one specific question, no, an EC does not have to be "certified in the program." The project can get one of the available points by having a person who is a "LEED Accredited Professional" involved in the design and implementation. But the project can only get one point in this way, no matter how many LEED APs are involved. To get that accreditation requires the person to pass a very difficult test. I have known people take the test 3 and 4 times, each time having to pay $250 for the privilege of taking the test.
To answer your more general question, the first thing you need to find out is whether the project is "registered" with the USGBC, and whether the owner plans to submit all the paperwork necessary to achieve certification. If is really is to be a LEED project, then the burden falls first on the "design" half of the design/build team. The "build" half of that team will have to follow whatever design and installation requirements are set by the designer, and will have to submit paperwork (e.g., purchase orders that prove the materials were purchased from a local manufacturer, proving that you did not spend too much gasoline getting the materials shipped from far away).
Oh by the way, I am a LEED Accredited Professional.