It IS possible to run SL on a netbook with an integrated graphics card... but the ridiculously low FPS rate makes it choppy and hard to use.
I have an older Compaq Mini 110c with an integrated Intel GMA 950 chipset and can run SL ok - but only in low-population sims (or skyboxes). I have Win7 / Ubuntu 12.04 dualboot and can run SL on either, even with Viewer 2 or 3 (not that I would suggest doing that - running a lightweight 3rd party viewer produces better results, and I've tried pretty much all of them except Henri's).
IF you run Windows on a netbook, I definitely suggest running your viewer through GameBooster 3 - it will shut off all your unnecessary background programs and just run the viewer. I've noticed about a 2x-4x FPS boost while doing this - still slow but I can render mesh and not crash, so that's a plus. However, if I go into any area with a lot of people I kill the mesh rendering just to make sure I don't freeze up.
I've yet to find a decent solution for Ubuntu. I've tried most viewers and still average around 2-3FPS (although the official viewer averages at around 1.5-2FPS, so a third party viewer is better). I haven't tried Henri's viewer yet, that's next on the list (I'm on my Win7 boot as we speak, not inworld but I was a few minutes ago).
I've spent FAR too much time messing with getting SL to run on a netbook, largely because I'm in a similar situation as you - my other computer crashed and I'm not really in a position to replace it at the moment, so my netbook is pretty much my only option right now.