Do you have just one 2" PVC pipe and need to pull 32 x CAT5e cables? That's just not going to work! You may be able to jam this many into a very short stub of a 2" pipe but that's not really a pathway, I'm assuming you need to go some considerable length, so that's not going to work. This is not even talking about any turns in the pipe, just a straight run will not work.
25pair CAT5 cables are rather rigid, they do not pull easy even though they may get you more pairs in a given crossection or a *straight* run. Since you need to come out of the PVC and into a floor duct at an unknown and inaccessible point, you need your cables to be as flexible as you can get so they can conform to an unknown radius turns better.
Do you have to pull all cables in the same direction after you passed this intersection of 2" and 4" duct? Or are the desks all around that spot?
Anyhow, suppose I did not understand you correctly and you have more than one 2" PVC pipe. Still, you are merging from a very thin pipe into an unknown fill ducts at an unknown and inaccessible point - this just begs for trouble. What is in the duct, anyhow? Is there an existing abandoned cabling you can pull out from that duct (charge the customer for it) and while at it, investigate the fill/layout of the duct, find any access points still available, learn the duct distribution to a degree that would make you more comfortable with adding new cable to it later.
Is the furniture sitting ontop of the duct? Where are you going to keep you intermediate connection points (those 66-type blocks)?
Given the unknowns of the duct, I would not commit to 5hr downtime deadline either.
Our ancient Helpdesk system does not allow adding text to the original question. If you have any additional info you'd like to share, just post another question referencing this one and we'll pick it up from there.
Dmitri Abaimov, RCDD