It probably would since your wireless is really slow, but it really depends on the wiring of your house. If your wiring is quite old, a powerline device probably wouldn't work, but if it's all fairly new...maybe if the house was build around 10 or less years ago then it would probably work fine.
I tried to use a powerline device in my previous house but since the house was probably at least 30 years old, the wiring was too crap. I'm now in a newer house and it works fine here (not at it's full capacity mind you, the speed LED says the power point I'm using works but is not great).
If you could somehow get your hands on a powerline device that someone you know owns, it would be best to test it before making a purchase.