Connecting both adapters to the same LAN will do nothing for you. It shouldn't cause any problems per say. Try it and see if Windows pops up any warnings. Typically windows will just give one adapter priority over the other and use it. Its possible it will keep both adapters active & load balance traffic for your outbound connections. You can verify this by opening a command prompt and entering "route print." If there are two default routes listed (route to 0.0.0.0 0.0.0.0) both with the same metric then Windows is actually load balancing your outbound connections.
One way or the other I wouldn't do it.