Spending varies greatly WITHIN districts, between schools. Money follows teacher salaries, and the highest paid teachers tend to be in the schools with the highest SES students.
With the possible exception of the well-funded Philadelphia and Pittsburgh school districts, most of Pennsylvania's school districts tend to be small, usually with one high school and a couple of elementary/middle schools. That's not much room for within district variation. I think we're going to lose much by looking at spending on a district basis, rather than a school basis.
As luck would have it, there is data for Teacher Compensation in the data set. Here's the definition given:
The total amount of money spent on salaries and benefits for instruction, support services, and other elementary/secondary programs. Compensation includes gross salaries and benefits for instruction, support services, and other elementary/secondary programs. Compensation excludes objects not directly related to salaries or benefits, such as purchased services, supplies, and debt expenses. At the district level, this expenditure includes only money spent on students taught in the district. It excludes money paid to other school systems for the education of students outside the district.
So, let's see what the data says about teacher salaries flowing to the high-SES districts. Let's compare teacher compensation to the percentage of low-SES students.
Now let's test the theory that high teacher compensation correlates with increased low-SES student performance:
I'm sure the causation here is complex. I'd guess that over-paying for bogus credentialism plays a role inflating salaries with little gain to show for it, overwhelming the higher performing teachers that leave the poor districts for greener pastures.