I've seen mention of some interesting studies done on balsa wood as a material for such instruments.  I very much doubt it could sound the same.  But it seems it can at least sound nice. 

I would assume they make only the top of balsa, since the neck, sides and back would have to be some tougher wood or material, I think?  I've also seen mention of instruments made with pine or cedar.  

I don't see where it would be much of a cost saving move, since one can buy a beginner acoustic violin set off places like amazon for as little as about 40$. 

Kind of interesting as an instrument to read about, but I would tend to think that using a drastically different wood for the top like balsa would take quite a few years to figure out the acoustics and etc to bring out the tone and even to learn what it takes for a *good* piece of balsa.  After all, the trad/wooden/acoustic violin is the product of generations of development and fine tuning of designs. 

But if somebody likes the sound and the feel of the instrument and wants to go buy one, more power to them.