Yes, but you must have Windows XP Service Pack 2 (SP2) or Service Pack 3 (SP3) installed to be able to access Windows Update website and update via Automatic Updates.
A few months from now, you'll have to have SP3 installed in order to be able to access Windows Update website and update via Automatic Updates.
WinXP SP3 (only!) entered Extended LifeCycle Support phase in April 2009. While security-related updates will continue to be available well into 2014, there will be no further "improvements" or added functionality.
~Robear Dyer (PA Bear) ~ MS MVP (IE, Mail, Security, Windows & Update Services) since 2002 ~ Disclaimer: MS MVPs neither represent nor work for Microsoft