Technically you can connect to both router one via wifi and one via ethernet if you want. You must make sure they do not use the same subnet when you do not have control of both routers.
Now connecting to them and using them for anything actually useful is a different story.
The key thing you can't do is combine them and get more bandwidth. A single file transfer is made up of a single IP and actually a single pair of ports. So there is no way to get a faster download...ignoring torrents.
In addition you can only partially use both connection because they have different IP addresses. Since they have different IP addresses they are considered different machines. The example that most people on this forum understand is say you were to log into the game site main server via ISP 1 and then you attempt to open a session on a world server on ISP 2. Since these are different IP the game company will think you are hacking and likely disconnect both sessions. This not just game companies, say a site uses a different server to process its credit cards and you place your order using ISP 1 and then attempt to pay using ISP 2.
SO if you really want to pursue this. The magic command is ROUTE.
What you want to do is DELETE one of the 0.0.0.0 entries. This is the default route. Now all traffic will flow over the link that still has the 0.0.0.0 route. You now can use the route ADD command to add in routes for the IPs you want to use the secondary server. So with careful planning you could use one connection just for your game and run your web surfing on the other.
In general it has extremely limited usefulness