But like Matt says, you could try it, and if nothing else sell the projector with a working bulb. Of course if I was the buyer of the projector, I would hope for a certain level of performance, and if the bulb was not able to produce a decent image, I would feel a bit shafted by the purchase.
But if you were buying a $2000 projector for $350, would you really expect to get pristine results from the unit?
Then you would be another $250 up towards you next projector. and the person buying it might also be quite happy with the results they are getting from what they paid.