Maybe, but probably not. Why take that chance? The cheapest Celeron I've seen is ~$50. And you're going to have to buy thermal paste for your C2D, anyway. Why not put $.20 worth of thermal paste on the Celeron? Because guess what happens if you don't get the BIOS fully flashed, before the processor burns up? That's right, you get to buy another Celeron and and then send your motherboard back to the manufacturer, so it can have a BIOS installed. Of course, it's your choice. Let us know how it goes, if you try it without any thermal paste.
edit: And if you were talking about running it without a heatsink, good luck with that. You won't even make it TO the BIOS, much less be able to actually update the BIOS.