It might work, or you could spend a lot of money on new wireless gear and it still doesn´t work as well as cable.
I would spend the time effort and money in pulling the ethernet cables through walls and under floors. A much better investment in my opinion
If you do want to go N, you will need to make sure all the equipment is dual band, i.e. it will use the 5GHz spectrum, this is far less likely to get interference from other equipment or near by networks.
The other alternative is Powerline networking. This can also suffer from issues with your home wiring and general performance issues.