Chicago has played host to many pre-Broadway theater openings and become the launching pad for a number of Broadway’s biggest hits.There was “Spamalot” in 2005, “The Addams Family” in 2010, “Kinky Boots” in 2012 and the blockbuster Mel Brooks show “The Producers” in 2001.Now “Paradise Square” the first big Broadway-bound musical to be offered since the pandemic, wants to take a crack at it.Running through Dec. 5 at the James Nederlander Theatre at 24 W. Randolph, prior to its opening at the Barrymore Theatre in March, this …