Well, your going to have two completely seperate gateways. 1 for your network and 1 for your neighbor's network. There is never a guantee on when it is using what and it would over complicate troubleshooting.
Also, some applications rely on a specific NIC to be used and this is setup during installation. I've never seen an application that could not be changed to use a different NIC but...ya never know.
I personally would not advise leaving both up at the same time. I'd also advise not using your neighbor's Internet connection. If you can easily connect, so can other people now you're wide open on a wireless network that has no security. You may think you have good host security, but it is very seldom that a savy person can't bypass OS security.
Anyway, what your thinking about doing is ghetto dual homing it...but without doing any ip routing functionality. So you have basically no control over which path your traffic will take. Frankly, I thought this was too basic and common sense and I've never done all out testing with it. If it is really that hard to plug the cable in or whatever, go for it. Just understand that you're complicating matters from a L1-L3 point of view.
My '03 Sold.