Jamie Oliver has previously recommened the use of a simple granite slab as a Pizza stone so provided there are no coatings etc. it is feasible.
You will need to be careful to start with though. Granite could shatter under thermal stress or due to trapped water and when it does so, it could do so in an explosive way damaging your cooker. You need to be sure that the board is granite as other stones may not be strong enough under thermal stress. You need to be careful of reconstituted stone as well because this will not necesserily perform the same as natural stone. Make sure that there are no signs of weakness in the board such as cracks or natural weaknesses. Make sure that the stone is thick enough to avoid issues with stress changes as the stone heats up.
If you are going to go for it, I would recommend initially do it slowly, start out with the over cold and heat it up to a lowish temperature a leave it for a while, then turn the over off and let it cool. Inspect the stone, check it for cracks or other signs of distress and give it a few light taps. It should 'ring'. Dull sounds are indiciative of cracks. Then go to a higher temperatures.