No, SonarQube for IDE flavor will not consume license code (neither when using the plug-in in Standalone or Connected Mode)
Yes, PL/SQL is being analyzed but not by every flavor of SonarQube for IDE, currently only the following flavors support it in Connected Mode only. Please see the respective documentation as additional requirements might be the case:
There is no SonarQube for IDE plug-in specifically available for typical PL/SQL-related IDEs if you have those (like PL/SQL Developer, Oracle IDEs, …).