A faster internet connection is always better, but DF Studio can be used for viewing and editing on fairly slow connections. The 1-up view provides setting for using smaller or larger previews and the thumbnail row along the bottom can be turned on or off to help tune the amount data being sent, according to your connection speed.
The connection speed required for uploading is largely dependent on the size and number of the files being uploaded. If uploading only jpegs, the connection does not need to be extremely fast. Uploading larger TIFF files requires a fast connection. There are online tools such as http://speedtest.net/ that can give you an idea of your connection speed.