If the HVAC system has fuel based heat (or fuel based backup heaters), then having the blower means having functioning heat in the winter, even if you don't have the compressor to provide air conditioning in the summer.
I would be horrified if someone were trying to run an central air system using a _fixed frequency_ inverter system. You have all of the power silicon needed for a VSD, but by running at fixed frequency you have all of the inrush current problems of an 'across the line' start. Talk about the worst of both worlds. Far better would be to run the motor using its own VSD supplied from the DC bus.
When operated on a VSD, the starting current to the motor can be maintained at or below full load running current. If the mechanical system is designed for fixed speed operation, then the VSD would simply act as starter and inverter, ramping the motor up to operating speed without an inrush current spike.
Working out the details of controlling such a system would not be trivial, and I don't know if inverter driven HVAC compressor systems are available for residential use, nor do I know if inverter driven HVAC systems come equipped for DC input. (Only some of the VSD systems that I've encountered have explicit instructions for how to operate them with DC power, though essentially _all_ of them have an internal DC link.)
I know that variable speed blowers for home HVAC systems are common in the highest efficiency gas furnaces. They add quite a bit to the cost, but that blower actually chews up quite a few kWh over the years. I don't know if such variable speed blowers could be easily modified for DC supply.
-Jon