Take a look at this article:
http://www.arrl.org/files/qst-binaries/ ... chmidt.pdf
and note the chart at the bottom of the first page. Good generator/inverter sets will produce 120V, 60Hz AC power with variations of 3% in voltage, 1% in frequency, and 3% sine wave distortion. Their unidentified cheap genset, according to the table, produced 157 VAC at no load, 15VAC at 500W load, and 149VAC at 1000W load. It may be that whatever you're running from your generator will take that voltage and not fry. The Honda EU2000i produced 126VAC no load, 124VAC into 500W, and 123VAC into 1000W. The frequency was 60Hz across the board, while the cheap one delivered 64Hz at all loads.
If your Pzap is comparable to the cheap one tested by ARRL, what will happen to your devices? Maybe nothing; read the device manuals to find out what they look for as to incoming power.
The other issue is noise. I think the EU2000i is offensively loud, although I'm assured it's quiet. The ARRL says it's 59dB at its rated load.
See if you can find specs for the Pzap, and also look for user reviews. Online stores like Amazon, OSH, or Harbor Freight may have user reviews and more information on the items they sell. Check out the Pzap on their Web sites.