Yes you can. Yes it has been done. And yes people are still doing it. The caveat being that most (all?) of the tests are done with scale models rather than full size planes.
Free flight wind tunnel tests are done for different reasons from static mounted tests. Where static mounted tests are done to collect measurements of forces acting on the aircraft/part, free flight tests are done to understand/confirm the stability of the aircraft.
Flying a model plane in such confined spaces is very difficult and typically the plane will tend to wander around in the wind tunnel. As such, the data that you can get from a free flight test is very limited.
Due to the difficulties of doing the test and the limited amount of data you can get from it most new plane designs don't go through such a test. Instead, what typically happens is that the design goes straight to a radio controlled scale model that is flown outdoors to study its stability. However, when trying out new ideas that has not been developed it is still worth doing the stability tests in a controlled environment - in a large wind tunnel.
Here are some old videos of free flight wind tunnel tests (these come from a time period where the behavior of delta wings were not yet fully understood):
Here's a more recent video of a free flight wind tunnel test of the Blended Wing Body:
answered Apr 14 '15 at 7:24
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