not in my experience - when I did a presentation on this back in 2009, the urban school district I was working in spent almost $17,000/year/student. This was a district that always scored dead last among the 450 or so upstate New York public school districts, in every metric that mattered.
$17,000 a year per student to achieve failing results
the adjacent suburban district that my kids attended, that I lived in, that I had attended when I was young always scored in the top five percent
my district spent 13,000/year/student
that's 30% more to achieve failing results