No, only Poohbah has just four BP agents in any given sector because Poohbah doesn't believe that a country with a $12 trillion GDP can afford any more manpower on the border.
The American public isn't willing to spend the money. Period. They'd rather have it spent on pork in their districts.
Second: absent immigration (legal AND illegal combined), America's population will decline. The only way to avoid this is to draft women into the Maternity Corps and order them to have babies, and after they reach majority, draft their kids into the Border Patrol. In short, unless you're willing to do those things, your policy is not sustainable in the long run (i.e., more than 20 years or so).