Does a Scanned Map have to be georeferenced in the projection of the original Source?

When viewing anything in a geographic coordinate system in GIS software, it is not unprojected. It still has to be displayed on your 2-dimensional computer screen. Usually this uses a latitude/longitude grid in a type of equirectangular projection known as plate carrée. This would produce a very strange result in your georeferencing, since your source map is a conic projection and the GIS software would be a cylindrical projection.

I would recommend making your best guess of the projection parameters. There's an Albers projection for India on SpatialReference.org that has some parameters you might want to try.