Do I already need to have a central HVAC system installed (working or not) in order to get a HVAC system installed through U2$?

An existing duct system is preferred but not mandatory. This is because ductless systems are offered through U2$, and in many cases, are less expensive to install (and operate) than traditional central HVAC systems. The best way to answer this question is “It depends.” This will be determined on a case-by-case basis during the assessment process.