Heliport
Yes it does. The FAA will accept a full license from a JAA state as satisfying their own training requirements, and after the flight test you will be issued with a full FAA license.
Thereafter, should you wish not to renew the other license (or indeed not be able to) then provided you meet the FAA medical requirements and recency checks, the license remains full and valid.
There is a strong case for having both licenses as independents, because you are then legally able to take advantage of whatever each may offer as regulations change.
Fly safely all