You should see higher speeds with wireless-n, but you would need more than just an n capable router, you'd need to swap out your g adapters for n ones to see any benefits.
Please note that should, the nature of wireless is that there are no guarantees, your new wireless-n network could perform flawlessly for weeks until a nextdoor neighbor installs his network and the resulting interference trashes your performance - or - you might see absolutely no change in performance - it just depends on the "wireless environment" where you live - or - you might live happily ever after - fairy tale style.