Your overall concept does work but your diagram setup needs more work and the details need a lot of 'fine-tuning'.
There are commercial products (eg CoolIT TEC chillers) employ the same principle: the cold side of TECs cooling the coolant in a chamber while the hot side gets cooled by an air cooled giant heatsink.
There are also a number of personal projects on this idea. One well documented one is: http://forums.vr-zone.com/project-lo...r-worklog.html
Read this guy's work and it is quite interesting. You may even use his as a starting reference and see if you can further improve his experiment, especially paying attention to the 2 areas of ''achieving optimal contact pressure of the peltier sandwich'' and ''sufficient power supply''.
Lastly I encourage you to research a little bit more. And I also encourage you to actually try the experiment when you have the time, money and some knowledge. Perhaps this can be an ongoing project if your interest in this subject is strong enough.
At the end of the day if an experiment is successful and yields satisfactory result, it is good. However, experiments are experiments and they also mean fun and educational. I think you will have a lot of fun during the process and will learn much.
Lastly, I suggest you start a new thread in the ''Cooling Experiments'' section (vs in this ''Peltiers/TEC'' section) which is a more appropriate place.