Here's one thing to try, I'm not sure if it would work or not.

Have person A get on battle.net and stay on. Have person B (different computer) open a command window and perform an ipconfig /release, ipconfig /renew. If your ISP dynamically assigns IPs, this might give him a new dynamic IP. Then he should start Starcraft + battle.net like usual. Battle.net could possibly be fooled into thinking that these were two different IPs. Either that or person A will lose his connection to battle.net. This probably doesn't have much chance of working, though.

Proxies will probably work, but man will your connection to battle.net be hella slow.