If you want to download or stream music and video with Lets-Box, you will stream the files directly from Box. So there are no bandwidth or file size issues for your web host. Only when you are using the gallery, the images will be downloaded once to your site to create the thumbnails and this can generate some traffic. The images will not be stored on your web server.
Please keep in mind that the bandwidth limit for Box Starter accounts is 10GB per month. Once you reach 10GB you can no longer download/stream via the plugin until the next month. However Box doesn’t strictly apply this limit bandwidth limit. So it more like a Fair Usage Policy.
The limits are quite low compared to other Cloud services. Dropbox has a limit of 20 GB per day for free accounts, and Google doesn’t even mention any limits. If bandwidth is important for you, you should try one of my other cloud plugins: Out-of-the-Box or Use-your-Drive.