Here's my take on this whole topic.
Scenario 1: Using a grid-tie only inverter with a solar panel may provide extra watts to start an A/C unit. However you're pairing two things and asking them to do things they're not designed to do. I think chances are likely that when the A/C tries to kick on the draw will drop the voltage enough to trigger the anti-islanding protection built into grid-tie inverters and the inverter will kick itself offline for a 5 minute timeout.
The solar panel will be unable to contribute any power when the generator is off. You lose any possible solar energy collection.
Also, even if it does work how are you going to get the A/C to run at night?
Scenario 2: Get a generator-boosting inverter that can supply the extra oomph necessary to start the A/C unit. This way you're using components designed for the job. Get a good MPPT charge controller and you can harvest solar energy sun up til sun down. Much more solar energy will be harvested in total and your batteries with the generator-boosting inverter will allow the A/C unit to start up even when the sun is down.
It certainly is an interesting "Hey, is this possible" question but I think it's far and away less efficient even if it does work. If you can repurpose the grid-tie inverter for another use if it fails in this combination attempt then by all means please let us know how it works out.
