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It will still output as process. You can confirm that by using the separations preview panel.
Okey, that's great but I would still like to convert all the spots to process in the swatches pannel all at once like I can with the script for rgb to cmyk. Any ideas on that?
You really don't want to do that, you just think you do. Redining the spots as process means they would need to be redifined again if you ever need to output them as spot. Using the ink manager is "effectively" doing the redfinition, and if you check the Use Lab Valus box it will even convert them to better mixes for whatever CMYK profile you choose for output, increasing the chances of a good match (since most spots don't convert will to CMYK). The built-in CMYK values are for some unknown profile that most likely is not the same as the one you will be using.
If you are using OSX try this AppleScript:
tell application "Adobe InDesign CS6"
tell document 1
set accurate LAB spots to true
repeat with a from 1 to count of every color
set model of color a to process
set space of color a to CMYK