It will still produce flavor and color, but it will take longer. I prefer to make sun tea in the sun because of how pretty it looks :-)

IrisIsIris is right about the bitterness. But my Oklahoma grandmother would put a pinch of baking soda in it to mellow it out.

Yes you can, but then it isn't sun tea it is refrigerator tea. What there is to love about sun tea is watching it turn colors!

IrisisIris, why did I not think of that teabag trick? I love it.

I cold brew (meaning, tea and tap water) on the kitchen counter all the time.

I will refer to my Okie heritage as my creds to answer this: No. You can brew the tea in the fridge, closet, backseat of a car, etc. Putting it in the sun brings out the tannic acids (a more bitter tea "bite") than doing it in a cool environment. The fridge brewed tea will not be as dark as sun brewed (or boiling water for that matter), so consider how you'll drink it; if it will be diluted with other flavors (sprig of mint, slice of orange, etc.) you may find the fridge brewed tea flavor too mild.
Bonus info: I put a single tea bag into one of those little bottles of water the night before a outing and leave it in the fridge. The next day, I leave the bag in and sip the tea - which also makes it easy for me to figure out which bottle is mine among the rest of the happy campers.

You can cold steep it, but it'll take longer. The sun really does heat up the water quite a bit, speeding the process.