A very astute question. Yes, as much effort goes into the design of the underside as does the shiny side.
The most recent article I found via a quick G search is from 2013. For sure the rules have changed since then, but it's still a fair benchmark to illustrate the complexity of overall design with regards to the aero.
There isn't that much teams can do on the underside of the car. A lot of effort goes into preventing air from "leaking" under the car in the first place.
While you don't see the underside of the car much (for obvious reasons), the occasional roll-over crash (or crane lift after a 'regular' crash) gives us a glimpse from time to time. Check out Nico Hulkenberg's crash at Abu Dhabi pay year for a good example.
https://www.youtube.com/watch?v=rUC2gDPiHEc