When you connect to a server, the server will recognize an IP address, sending return information to that address specifically. The second connection would go completely unused with regards to your connection to the server in question.
However, if you lost your connection, you could re-connect on your second line instantaneously without having to wait for the first line to come back up. You'd just have a different IP address.
If say you wanted to download digital content from a specific address on one connection and play Freelancer on the other, this would allow you to continue playing your game without the additional packets from content unrelated to Freelancer interrupting your gameplay. It would keep your ping stable and packet loss from Freelancer to a minimum. This is a significant job setting this up, but the same effect can be achieved with my suggestion below.
Your easiest option by far (and the cheapest) is to simply have two jack-points installed for the individual lines coming in to the house and a separate router for each allowing you to manually balance what content is downloaded or uploaded on either line individually.
For example. Your seedbox could be on your 100/100 fibre connection, connected via a router which also served household wireless networks to keep browsing and email and streaming internet TV, (and other mundane tasks) away from Freelancer. A second router would provide you with a dedicated ADSL/VDSL/Cable connection (or other) specifically for you and you alone on a totally separate uncongested connection.
It's far easier to set up prioritization rules on a single network to allow Facebook/Twitter/YouTube/Internet TV first priority over torrents and other content than it is to use a single balancer across two networks designed to do totally different things and make rules so neither network never ever interferes with one another.
Disclaimer: I'm really sick right now. I hope that made sense.
