Webley,
Theoretically yes...your idea will work. However, not with these UPS units.
Cheaper UPS units (like this one that we're talking about) use an approximated sine wave (also called a stepped sine wave). This will run your computer and other electronic equipment, which will not know the difference. However, when power goes out, the second UPS in series with the first UPS will see this approximated sine wave as an unacceptable power source, therefore causing it to go into battery powered mode. This will in turn net you the same running time as if you had only one UPS.
In order for this idea to work, the first UPS in series would have to output a true sine wave. Models that put out a true sine wave are usually the upscale/server class (read "expensive") UPSes (Such as APC's Smart UPS series). In the case of a power outage, the second UPS in series would not be able to tell the difference between line power and power supplied by the batteries on the first UPS. Therefore, after the first UPS ran out of power, then the second one would kick in.
Just in case you're wondering, I have personally tried this scheme and had this experience. If you want to know the difference between a true sine wave and an approximated (stepped) sine wave, please ask in the Highly Technical forum.
Hope this helps!