I'd be concerned with the cooling capacity of that, honestly. Even if you can get the airflow around it, the contact patch of that doesn't look to be big enough to do a lot. Maybe I am not taking into account the circulation due to warm beer rising and cold beer falling inside the conical. Or...
We could always just do some thermodynamics!
1W = 860 calories/hr
Heating / Cooling 1g water 1 degree C = 1 calorie
1L water = 1kg water = ~3780g / gallon water (note, beer density is more but we will assume water for sake of sanity)
So...
Assuming a 60W peltier at 100% efficiency.
60W = 51600 calories / hr
10 gallons water (assuming conical is not full) = 37800 g
So, you could theoretically cool 10 gallons with a 60W peltier about 1.4 degrees C per hour IF you didn't have any outside / internal forces acting upon it.
The problem is, you do have outside and inside forces working on it (and I'm using a less dense liquid than beer to do calcs). And, not to belabor the point, the yeast at high krausen are probably creating half that much heat, if not more. Couple the yeast with the environment (remember, the environment strives for equilibrium) and your peltier will probably not keep up.
My 2 cents.
EDIT
Just saw brewzombie's post. Indeed, it will cool, as thermo (hooray!) has proven. But, insulating a conical that's producing heat may well defeat the purpose...