Another thing you should keep in mind..
Depending on how the monitor is designed, the use of a cheap 100W inverter may result in minor display problems while it's used. When used at home, the outlet provides a fairly clean sinusoidal signal. If you look at the output of one of the cheap inverters, it's rather choppy and square-ish. This is acceptable for laptops since its power supply converts it to DC anyway, but I'm not 100% sure about CRTs. Some monitors may be more sensitive to that sort of thing.
So basically, there is a possibility that it will look funny even though the monitor may be fine. Maybe someone else here more knowledgable about CRT design can tell you for sure... but it's something to keep in mind at least.