Yes. There are instructions for adding files to your Nook Color in the user manual that involve hooking it up to your computer with a micro-USB cord. You can also download books directly from CurrClick to your Nook Color. Here's how.
From the web browser on your Nook Color you can browse CurrClick and make a purchase, or visit the My Library page (in My Account) to download a title you have already purchased. When you tap to download the file, the web browser will prompt you with a new window telling you the download is being prepared. It may seem to hang for a minute at this point, but as long as your connection is good, the file will download. You'll be able to find the file on your Nook Color in My Files > My Library > My Downloads.
PDF files with a lot of artwork may render slowly, so be patient with those books. If you run into files that will not display at all, you can try to download them on your computer from My Library on CurrClick and transfer them to your Nook Color via USB, and if that doesn't work please contact us to let us know.