Sure, but it would get built (AKA: doing the jobs our citizens don’t want to do) and, when complete, the citizens can just turn around and go home, where they belong.
The USA will pay them minimum wage to work and then go home.
That, my friend, is a free-market business plan.
There is no universal right for any human being to be provided the largess of another sovereignty simply because their country can’t provide it for their own citizens.
So, your plan is that illegal aliens will build the wall?
Your plan sounds an awful lot like what a lot of American businesses are currently doing and what we want them to stop doing.