In short, no. At least, not a backpacking tent. These are all made of nylon or polyester, and any stove pipe will melt that stuff like a laser through butter.
Canvas tents are another matter. You can get a smallish canvas-wall tent (eight-by-ten footprint) and install a wood stove in that. Davis Tents, for instance, will sell you both a tent (between $290 to $400, depending on canvas treatment; www.davistent.com) and a small stove specifically designed for use in tents ($305). For my money, a good canvas tent would be warmer in the winter, anyway. There are other options. A company called Zodi makes a whole line of propane-fired tent heaters and water heaters, and the heaters can be used with any tent. That's because the burner assembly is kept outside the tent, so there's no risk of carbon monoxide and no flames inside the tent. A metallic tube delivers warm air into the tent. The smallest unit, about right for a tent the size you mention, goes for $140it burns off the standard propane bottles found in any outdoor store. The downside is that it does use a fan, so requires a battery, which is recharged from a car battery... and there you begin to see some of the difficulties.
Lead Photo: courtesy, Zodi