I think the best method to do this is to convert the data to a value of pop density per sq km (I am assuming the xy coord system is meters).
The expression below converts population (persons in cell) to pop density (persons per square km) in each cell.
popden = popcells / ((30.8 * 30.8) * 1e-6)
Then, no matter the cell size, when you run zonal statistics with MEAN you get an average population density. Multiply the zonal mean by square kilometers in the zone (you can calculate this value with Zonal Geometry) to get the number of people in the zone.
You could get an 100m grid with number persons by setting the cell size to 10, aggregate popden by MEAN with a factor of 10, and multiplying (with raster calculator) by 100 x 100 * 1e-6 sq km / cell, but I don't see the purpose, as popden can be aggregated at any cell resolution (including the original one) without any issues.