Quantify the difference between your original color and your converted color. If the Delta E is within tolerances, green light for reproduction!
The CMYK and RGB values are obtained according to the type of profile associated with the conversion. The sRGB profile will return RGB values, while an ISOCoated profile will return CMYK values.
What will be the best intent of rendering to obtain the match with the closest Delta E? Try it out with the many modes available.
Choose from the three Delta E calculation modes available to perform calculations according to your standards.