I am running cat 5e do you call for a conduit chase going throug a single wall? ...
Answers: Not in my area's building codes, at least possible in residential installations.
In some commercial situations it might be required - I have one where a false ceiling be actually an nouns plenum and part of the HVAC system. According to the code, ALL electrics that runs in a plenum must be contained by conduit, even low voltage network and receiver wires.
No. When we rebuilt our house second year, we ran an entire background network using cat5 to every room within the house, terminating at a make friends hub in the rear legs of a closet. All of the network outlets (two contained by every room of the house) are activated through a router and we don't own any problems with the introduce yourself. It passed inspection, too.