No. The actual number is completely unknown: the 1-to-19 ratio is one group's best guess.
First off, you have to take into account: nobody has an idea how much the wall will cost. Government projects tend to be like that; you only know the final price tag once you've finished paying for it. So if the final cost is, say, 20 billion, that 1-to-19 ratio suddenly balloons to 1-to-76. Aka, it's off by a factor of 300%. Heck, a budget overrun of only one billion would still make the 1-to-19 number off by 20%. To give an indication how little certainty there is in this '5 billion number', check out this article by the NYT, where the estimates for cost range anywhere from 21.6 billion to 70 billion. As an additional example, the 2006 Border Fence was estimated to cost 1.4 billion... but the final deployment price tag was 2.3 billion (64% overrun)... and the upkeep over 25 years was pegged at 50 billion.
Second, you have to understand that it's based off the affect the border fence had. Which means we have to somehow have accurate numbers of the effect it had. I giggled quite a bit when I saw this in the linked article:
The economists calculate it reduced the number of Mexican workers in
the US by 82,647;
... yeah, I'm sure all those digits of that number are significant. They had the effect measured down to each individual attempted border cross. So you also have to have faith in that number - if you think that number is understated and the real impact was more like 300k, then the 19-to-1 ratio goes down to 5-to-1. Here looks to be the article that first spawned the 83k number, and you can see that they arrived at the number by estimating how many illegal immigrants they expected before all this started, counted the amount afterwards, and attributed the difference to the fence. I don't know if there are any better ways to get an estimate for the effect, but to pretend the end number is extremely accurate is a stretch.
Third, since it's based on the fence... you have to assume the think-tank's modifications to effectiveness are accurate. I mean, the first thing to consider is the 'fence' consists of 350 miles of actual fence, and 299 miles of vehicle barriers... on a border that's 1954 miles long (33% coverage) - so how much would 'complete' coverage change the effectiveness? You're assuming their estimate of that affect is correct. Second, the fence is presumably easier to circumvent than the wall would be. How much easier? Well, you have to assume they've got that number nailed down, too. Third, the wall will cost more per foot than the fence - what's the difference in cost/effectiveness between the two different types of barrier? Again, they have a mathematical model for you; you just have to assume it's accurate.
Basically, what you're left with is something like:
There are 200 alien civilizations in the Milky Way; researchers uncovered this by using the Drake Equation
... aka, a nice easy-to-digest number... but that's determined by a huge array of assumptions and best-guesses.