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.
Right now this ground effect has been banned and it is mostly flat, except for some things in the tail.
The rear diffuser is sometimes blocked from cameras when the car is parked. For example 2009 with the double diffuser.
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.