I've got one and use the hell out of it. It's awesome.
Never built a balsa airplane, though. It's a pretty precise unit when you use a nice blade, but it's still a blade attached only on one end. That said, I've cut more acrylic on this thing than I can remember, and it's always been fine.
I think the biggest problem there might be finding the appropriate blade.
Thin, weak materials tend to like either a supported blade, or a circular blade spinning against a supporting platform. That leaves you with scroll, band, or table saws in general.
So, thread side-note: The Rockwell Blade Runner is wonderful and just as portable as they advertise. It's strong, precise, and well-made at the price.
I just don't think it would like that super thin balsa wood. I'd stop by the hobby shop to grab some and give it a try, but I'd still need an appropriate blade, and all we have nearby is a Lowes.