Yes, with the driver that is shipped with version 10.1 of Mathematica, as long as you also have the Arduino software installed (you don't have to manually open it), Mathematica can upload the sketch to the Arduino by just evaluating
DeviceConfigure["Arduino" ,"Upload"]
If you don't have version 10.1, then you will need to upload the sketch and use the package as I detailing in my other post, http://community.wolfram.com/groups/-/m/t/315748?p_p_auth=haouzG0j.
Ian