Not really.
The HTTP adapter is not capable on maintaining a session for multiple sends. You would have to determine the session mechanism of the web site (cookies, hidden form field?)
You will need an orchestration to send a login on message (a Form Post, effectively a flat file) that you would have to create. Then retrieve the session token from the resultant HMTL (you will have to write the code to parse the HTML). Once you have the session token you would be able to send another message.
All this becomes very cumbersome in an orchestration. You could write a custom adapter that would perform the logon and send in one send.
What is the purpose of logging on to the web site, are you sending or retrieving data?