AFAIK, many teams do static tests. Besides helping to solve world poverty they try to answer axle's question, or so I think.
Here is a picture taken from Automotive Testing (quite old, November 2005, Michelins on board, sigh) showing a static test (static from the point of view of the air) on suspension alone. This's Instron. Notice the red thingies, that can (or cannot) simulate the effect of the wings. So, there you go: you can do it with or without it.
Is using this or using extremely small wings, like the ones Red Bull gives you. I imagine they open the roof when it's raining, to check for wet conditions. Ha, ha.
There are rigs where the tires rock, roll, yaw, turn, shake and twist, before somebody points out that the wheels don't roll.
For some gratuitous self-promotion, I have a webpage (more like a "notepad" instead of a page) with some driving simulators, which you can browse in awe at
http://www.ciropabon.co.nr/ (go to links and then driving simulators). No congrats, I blush easily.
Now, it's just me or does "checking the rigidity of your structural member by shaking the whole thing on the wet with low downforce" sound like soft porn?