Technically yes, but you pick up viruses and spyware parasites from the Internet from your email and websites you go to so if you limit where you go to till you get ever thing in place you will be ok... the problem is once on the Internet a preexisting virus or spy ware parasites can come active but you need to get the latest updates for your antivirus,antispyware and OS to kill and protect you from the latest threat (Note if you have a something that keeps coming back... some really nasty viruses and spyware can only be totally killed in "safe" mode and with system restore turned off and there are some the even require special fixes )
... The thing is it's not a who came first the chicken or the egg the there are alway new virus, spyware or OS security crack that come first and the antivirus,antispyware and OS patch comes after (sometimes weeks after)to fix.... that why you need check you updated(On my antivirus I sometimes get 3 or 4 new auto updates a day)
Let me add one more site http://www.grc.com/ to check your firewall at... also besides a software firewall I alway recommend a hardware firewall router (Linksys or Dlink) on any alway on DSL or Cable modem Internet connection, they NAT the IP address to your computer to private IP address that will not pass over the Internet, bottom line the only public face you show (if any) to the internet is at the public IP, WAN side of you hardware firewall router (and change the default router password!)