About the third batch of beer I ever did, I wanted to do this too. I just couldn't not constantly check to make sure the yeast were doing their only job. Fear of contamination far outweighed my obsessive curiosity. In the end I came up with a great idea...after pitching the yeast I pulled a sample and put it in a large graduated cylinder, put a hydrometer in wort, and placed some foil over the top.
I was able to watch the fermentation process and the hydrometer level drop as it approached completion. I would never use this as a tool to determine if the beer is done or not. It was just cool to watch.
Today I just set it aside for three weeks then drink some beer.