I don't think a masters in econ makes up for an insufficient math background. It can help to "make up" for poor grades as an undergraduate, attending a less-than-stellar undergraduate university, having an undergraduate degree from a different country (or in a different language) than where you want to attend graduate school, not having taken many
econ classes, and, possibly, not having good recommendations/connections.
I've said probably everything I have to say on the question of masters degrees on
this thread, ("Get an MA" --> not one-size-fits-all advice) and other people added very useful comments. You might take a look.
But the bottom line is that math is one piece of the puzzle. Not having taken lots of math is a strike against your application, but is unlikely to absolutely black-ball you by itself. There is no perfect applicant. The admissions process is always about balancing qualifications in many areas, of which math is only one. Having very strong credentials in other areas (great grades, other rigerous classes, research experience, a publication, etc.) will get you considered for admission even without a lot of math. (I had not taken anything more difficult than multivariable calc when I applied, though I did take real analysis the semester before I began my PhD -- and I'm darn glad that I did!)
The level of math in masters programs is, with a couple of notable exceptions, including LSE, substantially below that required in PhD programs. First year econ PhD classes are proof-based classes. That's a mathematical technique you are unlikely to develop in a masters program in the US. You
can learn it when you start your PhD, but it makes life harder. I don't think a masters in econ is the most efficient or effective way of remedying a lack of math, either for application or preparation purposes. The masters in econ has its place, but I don't think this is it.