If the color is 0R 0G 0B in Illustrator, it can be mapped to 100K in Acrobat using Preserve Black.
In other words, the AI is output as PDF with no color conversion. The PDF is converted to CMYK in Acrobat Pro, with Preserve Black enabled.
I would stay clear of an RGB workflow for print. If you want Black text, then use Black in your color palette, not a CMYK combination. In preferences, or color settings, select Use Accurate Black.
Here in another solution.
If an Illustrator file is RGB, you cannot have CMYK process colors. But you can have CMYK defined spot colors.
You can create a spot swatch, CMYK, and make it any CMYK combination you want, including 100K.
Two choices after that. Place the Illy file in InDesign. In Ink Manager set "All Spots to Process". Then output a PDF.
Second choice – save as PDF from Illustrator. Use Acrobat to convert the spots to process.
The RGB process content can also be converted to CMYK on output from either Illy (save as PDF) or ID (export to PDF). Just convert to the destination CMYK.
Or you can choose not to convert on output, and instead convert the RGB in the PDF to CMYK using Acrobat.
A bit convoluted and error prone but usable. I just need to up the quality control around here and train the staff and wait for them to stop whining and whimpering.