Short answer: No.
Long answer: There is a menu for login / logout passwords on a KeiTama (regular and Akai-series), however the KeiTama doesn't actually connect to a web site. As far as I can tell from the instruction manual (page 20), it connects to an application called "Tamagotchi Park" that you have to download and run on your cell phone. I'm fairly certain this app runs only on Japanese-language cell phones.