Yes, a leaf blower will certainly be well over 500W, I'd say.
If you think about it, P=VI.
If using the maximum output, P=500W
V= 12, nominally (maybe 14 with the engine running).
That gives you 42 Amps, not accounting for the efficiency of the inverter, which will sap some power.
If it's an average battery in good nick it might be 60AH, so you'll kill it completely in 90 minutes, and I doubt you'd get much more than half that and still be able to start the engine afterwards.
Standard vehicle batteries aren't designed for deep discharge either, so won't take kindly to this sort of treatment.
The alternator should cover that sort of current draw, but might not with the engine idling. It might need a few more revs (or a smaller pulley on the front).
Also bear in mind that the inverter will shut down if its' input voltage drops below a certain threshold and, bearing in mind the large currents it can draw, the wiring back to the battery needs to be as short as possible and as thick as possible to avoid the inverter dropping out due to low input voltage.
An alternative to leaving the engine running might be to fit a leisure battery near the inverter and keep it topped up from the vehicle using a caravan split charge relay. You won't have to worry about running it flat, as you'll still have a battery that'll start the car.