Hey! I'm not an expert at all, but I did successfully swap out bars and change out a trigger index shifter for a friction thumbie this summer. My answer would be that yes, it would be a good idea to get new cables and housings for the drop setup. The incidentals kits that Riv sells are great, btw. Could I have reused the shifter cable? Maybe...the issue, though, is that even a VERY clean snip of a cable could have a frayed wire...a frayed wire will not pass through a housing when it comes time to set up the brakes and shifters. I actually REALLY screwed up with my first attempt (wrong cable pass under the BB) and had already snipped and capped the end of the derailer cable)...so I had to pull it back out and redo it...capping the cable caused it to fray a little, so I I trimmed it again to get a clean cut, crossed my fingers and held my breath, and re-routed the cable through the shifter, front end housing, and through the derailer housing and it thankfully worked.
The bigger issue is he might need more cable in a drops setup than in his current setup...and that calls for a new cable.
I'm rambling...but I just think it's better to have a fresh cable that will definitely be long enough.