I'm afraid you can't do that. Because the Multitrack time line defines what happens, all individual time references that applied to your audio clip when it was in its original position in the file it came from don't apply any more. If you import a section of a file into multitrack that contains markers, then you will see where they are - they appear as dotted vertical lines. These only indicate where a marker is relative to the other markers in the file, though.
What most people do is to create marker ranges, and give those ranges sensible names in the Marker panel. These will stay with the clips when they're imported into Multitrack view. This is the basic way that Audition is intended to operate; you select the parts of your file that you want to use, put marker ranges around them, and import these into Multitrack, where they can be rearranged.