Yes you can rent box just for this but if your speed is slow it will be slow when you are transfering data from box to your local computer too so it may not work like you wanted but yes you can.

I recommend you yo use seedboxes.cc. batbox is very good for your condition and also have plex media server support which you can watch movies in your box without downloading to your local computer. Plex media server installation is very easy and there is very simple how to do guide.