It is possible. Eclipse runs just fine (even on a first-generation single core Atom). But it is different from a "real" workplace and I wouldn't recommend it as main developement computer, just as a complement.
The processing power and memory is fine for just working with source, i.e. the normal text editing, showing Javadocs, call hierarchy, usages etc. But you certainly want to switch of continuous building and validating - which means that you find some bugs at build time only instead of when editing or writing the source.
The screen estate is lower, so you can't show all the views you are used to at the same time. Javadoc, declaration, call hierarchy, markers, outline, Spring outline, JPA details and so on - one at a time and switching. Or calling the quick outline / type hierarchy. No second screen for documentation or surfing parallel (obviously).
The keyboard is smaller than a normal keyboard - acceptable for short periods but not for the long run.
You see, it is a compromise. You give a lot for getting the mobility.
That said I program at a netbook (first generation, single core, 8GB SSD) frequently. It works fine if mobility is the key property.
But today there is a great number of small notebooks ("subnotes") that are a much better fit. Main differences: Faster processors (even if not on par with desktop variants or bigger notebooks), full-size keyboard, higher resolution, more memory. One of the most mobile ones of that class would be the 11" Macbook Air.
Oh, and
there are people with a name who use a netbook as main developement system (and thinking about switching from 9" to 10"!). But then Java developement needs more than an Emacs to be fun.