The state National Emergency does NOT need to be in effect for the duration of the construction.
Here is the definition of 'National Emergency':
The United States Code (Title 42, Chapter 68, Subchapter I, §5122), now defines emergency and major disaster as follows:
"Emergency means any occasion or instance for which, in the determination of the President, Federal assistance is needed to supplement State and local efforts and capabilities to save lives and to protect property and public health and safety, or to lessen or avert the threat of a catastrophe in any part of the United States. Source
The declaration of a National Emergency gives POTUS 136 additional powers, most of which are pretty boring.
Here are some relevant ones:
10 U.S.C. § 2808 (a)
Secretary of Defense, without regard to any other provision of law, may undertake military construction projects, and may authorize Secretaries of the military departments to undertake military construction projects, that are necessary to support such use of the armed forces (1982)
In other words, POTUS can order the military to build the wall without waiting for any laws to be passed by Congress. By declaring a National Emergency, POTUS is effectively saying that if Congress doesn't want to allocate funding for wall construction, he's just going to get tell the military to build the wall and there's not much they can do about it.
33 U.S.C. § 2293
Secretary of the Army may terminate or defer any Army civil works project and apply the resources, including funds, personnel, and equipment, of the Army’s civil works program to authorized civil works, military construction, and civil defense projects that are essential to the national defense, without regard to any other provision of law
Which means, POTUS can transfer funding, workers, and equipment from other Army civil works projects (roads, dams, bridges, maintaining training areas, things that the Army Corps of Engineers routinely works on) to building the wall, and there's not much anybody can do about it.
If Congress passes a law allocating satisfactory funding for building the wall, POTUS can then build the wall by hiring construction companies for the project, take the military off the project, and cancel the National Emergency even though the border wall has not been completed.