Colour profile management

images to PDF from InDesign to send to a printer in a certain CMYK colour profile, should the rest of the Adobe applications be set to this profile as well for consistency?

you don't say 1) what your original document and object source profiles are, 2) if you are doing any profile conversions in your export process, or 3) if your printer CMYK is a device-specific profile that you use exclusively or case by case

but, most important for managing your profiles and maintaining color "consistency" across proofing devices like monitors and printers -- within Adobe applications -- is to set all Adobe application Color Settings to PRESERVE EMBEDDED PROFILES and enable their PROFILE WARNINGS so you know what's going on with your profiles...

In a word, yes. But keep in mind the differences between a true black and a rich black and how that could affect elements in your document (which I know nothing about):

Rich black versus plain black

CMYK "Rich Black" information and Tips