There might be some terminology confusion possibly.
Anyway, the popular tool for checking all the meta-data in a file is "ExifToolGUI" - Google for that.
Here is a screenshot:
I selected ALL and scrolled to the ICC tags and, rightly or wrongly, it does use the phrase "ICC profile". Some apps embed profiles, some do not, and some offer the option.
I did an experiment in RawTherapee:
Saved a file with no ICM profile: ExifTool showed no ICC tags.
Saved same file with a profile containing A2B and B2A tables: ExifTool showed it to be present.
First saved file size was 679Kb, second was 859Kb - so 180Kb of
something got embedded, eh?
ExifTool by itself is a command-line utility which is made much mo' easier by downloading the GUI in addition, as you can see.