That question isn't as easy to aswer as mostly here think.
The raid itself wouldn't last very long, because the mechanics weren't that challenging BUT the most brutal about classic Naxx wasn't the raid so much, but rather the way reaching it. To properly gear your char to even stand a chance to kill Flickwerk you had to be geared to the teeth in the previous tiers.
This means going through ZG>MC>BWL>AQ20>AQ40. Considering that each Boss dropped 2-4 pieces per Kill for a Raidgroup of 20-40 this would take a while.
Most people didn't even set foot in Naxx cause they lacked the time and dedication to go through all of this just to wipe several times at DPS check bosses.
If you leave out all the gearing and/or gear via Badges or Worldbosses aka Tanaan, and considering most Top Guilds would have spend hours o the PTR to figure out tactics. Lets say you got properly geared Chars before the relase..It will most likely last a couple of hours. Or a couple of Days max.