dc/ac inverter

Yes

No.
Because the wind perhaps goes to zero for a long time.

And yes.
If you use an intermediate DC link by storing enough energy to bridge those gaps, usually done by large batteries.

Regards Uwe

If we want a pedantic argument then ..

Yes... as long as no load is drawn!...

Sorry getting silly!

Yes! But it's probably more cost effective to fix the generator.

Yes. Fix the generator.

Yes as long as the DC voltage remains above the inverter's minimum acceptable input voltage. You would need a regulator to keep the voltage at a constant level.

Now to the practicality of such a system. You really need to use your generator to charge a battery and allow the battery to provide the constant voltage and current to your inverter.

Increasing battery capacity will increase the inverter output time if the load remains constant. The downside to increased battery capacity is the greater recharging time to full recovery.