No, it is not possible to print a web map directly from the ArcGIS Online map viewer as a PDF. The map viewer only uses MAP_ONLY and PNG32 as the output formats.
The map viewer, not the print service, prevents this operation. For a different output type, use a different client or an application with more printing capabilities, such as the following:
For more information about configuring a custom print service with ArcGIS for Server, refer to the following ArcGIS Online Help document, Configure utility services.