Can I put an electrical conduit through this space above the wall to simplify future fishing?
Yes, this is a good idea, but a few details.  


No more than four cables per conduit, unless you're willing to upsize ALL the cables to the next larger size. That is 310.15(B)(3)(a). 
The conduit needs to be fairly large, because the cables are oval. Each oval cable is treated like a single wire of the wide dimension (because they twist). They can't fill the conduit more than 30% (for two) or 40% (for three or more).  1-1/4" conduit is probably a safe choice, though 1-1/2" will be easier to pull.  (pulling stiff Romex is a bugbear).  *This is not a Code requirement per se, but it'll surely be a practical limit given NM-B tends to have kinks, and kinks snag like crazy in conduit. 
Flex is a bad idea.  I know it seems easy to install, but the flex will fight you every inch of the way. The energy you are using to push or pull the cable will instead bend the conduit sideways. Believe me, this is very frustrating, especially when pushing, and pushing is (otherwise) easier since you only have to watch one end.  With a non-flexible conduit secured at both ends, that's an non-issue.  
Assemble the conduit first, then fish the wires through it.