Is it possible to convert an RGB image to CMYK without an ICC profile?
Short answer: If you don't mind which colors the CMYK channel values represent, simply apply any random CMYK profile you can find and call it a day.
Long answer: there is no really color space called "CMYK" with the meaning that ANY value combination for channels
K results in any specific color. Sure, a high value for
Y and zero for the other channels should output some kind of yellow. It could be reddish or greenish, dark or very light, you cannot know. It all depends on the ink and media used for output. The same can be said about "RGB" colors but usually you can take it granted that "RGB" really means
sRGB which is a real color space with a strict specification. An ICC profile for CMYK output device describes the end result of ink and media combination for any value combination for channels
K. If the intended result is to get similar color from the CMYK device as RGB device, you need to use correct ICC profiles for both. Most of the time, the end result will be really close even if you just apply official sRGB profile to the source.
If you don't know the profile of the output device, doing "color separation" (converting from sRGB to unspecified/random CMYK color space) is pretty pointless, in my opinion.