This is a tough one, because it is hard to determine how the employee numbers are distributed throughout the grid polygon (i.e. are they spread equally across the polygon, are should some areas of the polygon be weighted differently than others?). Off the top of my head, the only thing that comes to mind is creating a custom BDS layer in the Business Analyst Desktop extension. You would use the Custom Data Setup Tool and select the proper apportionment method. You could then create your trade areas of 1 mile buffers around your cities and use the Spatial Overlay (Append) tool to grab the values from the Grid. Then, depending on what apportionment settings you have set up in BA, you should see different numbers. The Advanced Apportionment Settings article discusses the different styles available.Unfortunately, all of this will only be doable with Business Analyst desktop. That's not to say there may not be some other way to get a similar result using ArcGIS without any extensions...
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