In my experience, no. Dropbox does not accept seed drives (like an Amazon Snowball). This upload must be performed by the host system. And the speed is limited by your Internet upload speeds. If you have an asynchronous line, then your upload speed will be slow. This will cause long upload times.
Also, if the data is on an external drive and you allowed the Dropbox sync folder to create on the internal, watch out for filling the boot drive. It is possible that your data from an external drive will exceed the capacity of the internal drive. Uploading to Dropbox in this case will first initiate a copy from external to boot. You will need to wait for all the data to upload and then set the data to online only. This will free space on the boot so you can do the next batch.
Hope this helps. I have the luxury of access to a gig synchronous with 10gig burst. Uploaded a customer's 110 TB of data in two batches of about 50 TB. Each took about a week to complete.
Reid