When checking your free Yahoo email address, it will not work over WiFi but it will only work on your carrier data network.
Now, if you have Yahoo plus with POP3/IMAP enabled then you could check your Yahoo email over WiFi.
What puzzles me is... you'd think Yahoo would want to compete hard against GMail. By making it difficult for users, and/or only offering it for a Yahoo Plus subscription, I think they're driving users away to GMail.
Just my $.02c.