does this or any software map voting precincts?

You could use the cartographic boundary files from the US Census Bureau to map the voting districts as SHP regions, importing them with the Spatial Data Import COM AddIn.

Census SHPFile
SpatialDataImporter

HTH
-Paul

Our company developed the Spatial Data Import tool that Microsoft posts for free download but it's not really an end-user product. However, we sell a tool that imports .shp files into MapPoint and gives you some formatting control over the imported geometry.
GIS Data Import for Microsoft MapPoint®

That product page also has links to US Census data for free download. If you go to those links you should be able to find additional files that we didn't list but that you can also import to MapPoint.

Regards,
Brett