I had to Google "Seedbox" first, because I'm not a filesharer. I'm buying things.
According to Wikipedia, some of these Boxes are using 'rsync'-protocol. That's in OMV too, so it can handle the Job.
On command line you could use 'wget'. Make a script and autorun it via 'chron'.
Or you can use your PC to pull from FTP to your share on OMV. I'm using that for the updatefolders on softwarevendors FTP.