I say go for it. If you have a steady temperature and readily available lighting, you should be okay. Just keep a watch out for pest. You'll be in good shape when it gets warm outside.

Tim

Attics generally have little airflow, are prone to temperature changes, and retain humidity. Peppers can use about as much light as you can give them, and they require quite a bit to be happy and healthy. Supplying that amount of light might be cost-prohibitive in itself.

Generally I would not suggest it, especially for the long term. Plus, Where does the water go if you spill it?

I would suggest a Garage or basement over an attic if you need to grow seedlings or overwinter plants indoors. Production of peppers indoors would require a High Pressure Sodium or Metal Halide Fixture for anything other than seedlings.