I don't know that it would hurt to spray clear coat. But, i wouldn't advise it - i coated birdhouses with clearcoat, and the coatings weathered and peeled, looked worse than doing nothing at all.

If you do nothing, the cedar ages to a gray color, and will still last a very long time (many years). I don't bother coating mine. If you want cedar to stay a yellowish color, you can use a stain made specifically for cedar.

I would check the diameter of the entrance hole. What is sold in stores as "wren houses," typically have only an inch or 1 1/8 inch hole. House wrens can squeeze in that, but carolinas need a 1 1/2 inch hole. Unfortunately, house sparrows can get in that hole as well, so you have to have the heart to tear out sparrow nests if they try your wren box.

I would not recommend painting. Paint will chip eventually, and a natural wood environment is more attractive to the birds from what I have seen. We have a formidable number of birdhouses and all of them are unpainted/treated cedar, after years of trial and error of what birds actually nest in. Some of these houses are 20 years old and in fine shape, left out year round in both Georgia and New England. Plus, they do turn a beautiful color with age!