Absolutely! The router hides your IP address. Any hack that runs through a list of IP addresses won't find your machine. It doesn't protect you from all sorts of malware that might find its way to your machine via the internet and email. You still have to protect yourself from trojans, viruses and all those other nasties.
The best thing you can do is stay away from dubious sites. If you only go to GWTW you'll be fine.
I also like McAfee Site Advisor because it will give you a pretty good idea if a site is okay or not.