I think the best reason to try the M Experience would be to try the other M cars and compare them to the M3. They may also do some skid pad time which you usually don't get at HPDE events.
You will learn,but it is comparatively expensive
2011 e92 M3 Monte Carlo Blue ESS 535 - gone but not forgotten
2015 cayman GTS - new toy
2006 SLK 55 AMG sold