Judging from the Eeschema file format, it doesn’t associate nets at the .sch file level. It’s only a collection of parts, labels, and wires. Pcbnew on the other hand associates each pin of each component with a net at the .kicad_pcb level.
It would not be a trivial task to add this functionality to Eeschema: you’d be better off writing a conversion tool to change Eagle .sch to Eeschema .sch.
Kicad’s project leader and some others are working on changes to Eeschema and its file format for the next release.