No, Airport is not broadband. Broadband normally refers to the connection to the Internet, not your Local Area Network connection. You could theoretically use Airport to connect multiple computers together, without any of them being connected to the internet.
And broadband is normally taken to mean anything faster than a 56Kbps dial-up connection. So DSL and cable modems are clearly broadband, for example. But also wireless internet services like Ricochet and 2.5G cellular services are considered broadband, even though they run only at a little over 100Kbps normally.