Strictly speaking, no you don't. Airbrushes were originally designed for artists, and they didn't consider airbrushes spray booths. Tshirt artist and helmet painters also don't use spray booths.
Think of airbrushing like cooking. You can cook anywhere you have an energy source. But it IS a whole lot easier to do it on a stove!
Paint vapors, overspray and your family's reaction to both should be taken into consideration. Also, having a vented, lighted and hopefully dust free area to paint makes the job easier.
Like Andy, I built my own, though I spent closer to $150, but it has ample light, awesome amount of room, acrylic doors and is vented to the outdoors where the vapors can dissapate harmlessly.
/edited for clarity