This is probably one of the most confusing areas of the NEC.
First, the sheath on NM cable is not sufficient to protect it against damage if "accessible", typically considered below 7'. You can legally run NM cable on the surface of walls and ceilings above 7' and inspectors won't complain too much. That said, I like to protect it any time it's not inside walls or ceilings.
Where it gets fuzzy is conduit fill rules. These rules require conduit to be properly sized to protect against heat build-up, and require the NM cable to be considered as a single conductor, and the conduit would have a fill limit of 53% -- this means the area of the conduit must be 47% greater than the area of the NM cable. For 6/3, it means a minimum of 1" conduit. Now, here's where the uncertainty comes in -- the informational notes say that conduit used as a sleeve to protect cable against damage doesn't count in terms of fill rules -- but there is nothing that specifies the characteristics of where a protective sleeve ends and a full raceway/conduit system starts.
It is true that if, at any point, the conduit runs underground or outside, that NM cable cannot be used because it's rated for dry locations only.
The bottom line here is that what you describe, I believe, is fully legal and reasonable if the conduit is 1". There may be questions if it's only 3/4" conduit, but in that case I'd applaud your ability to pull a 650 mil cable through a 750 mil conduit without too many swearwords.
Finally, it should be noted that this is an area where local amendments frequently apply, so contact your local city / county inspector. In Chicago, for example, it's illegal to use NM cable at all.
