So I have Illustrator document in CMYK mode intended for print. I need to import PNG image (because I need to place object extracted from the background). And here I step on the unknown area because I actually don't know will Illustrator automatically convert PNG image colors (which is RGB only format) to CMYK.
In Illustrator's Color settings, working CMYK profile is set to "U.S. Web Coated (SWOP) v2". In Color Management policies my settings are: -RGB: Preserve Embedded Profiles -CMYK: Preserve Numbers (Ignore Linked profiles)
When saving new Illustrator document, Embed ICC profiles is checked. When send to print, I export PDF with "High Quality Print" settings which, as far as I know, is set to embed color profiles.
Because I usually have no direct connection to the printer, my ultimate goal is to find and use default workflow, which will work in most situations. I spent numerous hours exploring colors topic, but still I am not so sure about each specific situation.