Legalities aside, a declaration of a national emergency won’t achieve what Trump wants, unless his goal is simply getting out from under the shutdown. That’s easy. He can say he’s going it alone under his emergency powers and agree to open the shuttered parts of the government, then fight it out in the courts.
But in terms of his substantive goal of building a fence, and his political goal of building enough of it to showcase in his 2020 reelection campaign, it would get him very little. A district court somewhere would immediately issue an injunction blocking the action.
Once the administration gets to the Supreme Court, it might have a chance to prevail if the court concludes that it shouldn’t second-guess the chief executive on questions related to national security. But when would such a decision get handed down? Sometime in 2020?
Assuming Trump wins at the high court, it would take time to get anything going on the ground. Progress on the fence probably wouldn’t be any more advanced by November 2020 than it would be otherwise, and perhaps less advanced than if the president simply got some inadequate compromise out of Congress.