Color Management
Inkscape's Color Management system allows documents to be created in color spaces and can help you create documents for printing.
SVG uses sRGB
When using managed color its worth noting that SVG uses sRGB as it's workspace color format. This can not be changed without breaking the SVG compatibility. When you express colors as CMYK colors, or import raster images, you will see the colors are converted to sRGB in order to be rendered to the screen.
SVG can use CMYK
But there are ways to supliment the sRGB colors with more information which allows us to store CMYK values. This allows us to output CMYK colors more faithfully, but does not produce exactly the same results as a CMYK working space would for example with gradients.
Spot Colors
There is a future plan to support spot colors, we will have to write here if we managed to get that to work.
Output Formats
Raster Output
Inkscape 1.4 onward support exporting CMYK color managed documents in both Jpeg and Tiff formats. All documents are rendered in sRGB and converted to the correct color management profile. You should use the correct rendering intent for the output to do the conversion and should always check the output in a third part program such as Cyan or Krita.
Vector Output
Inkscape 1.4 onward supports exporting directly to PDF with the CMYK color profile you have chosen. There are two important limitations which it's worth baring in mind:
Any raster images included in the export may have their color format changed in order to fit the deviceCMYK profile being used and you should make sure your rendering intents are set correctly.
Any filter effects such as blur, are not expressible in a PDF and must be rendered to a raster image first. These raster images will also have to be converted from sRGB and will incur the same rendering intent consideration as the Raster Output section above.