You'll need to turn on firewall logging for this to work, but yes, it looks like it's possible. You'll want to set the firewall to record successful connections, as described in this TechNet article, plus something to go through the logs afterwards and pull out the stuff you're interested in.
It seems an unusual way of doing it, though; do you really want the logging to take place on the same box that's doing the accessing? I'd go for something outwith the server you want to monitor that could log connections from the server's IP instead. Depending on what you use for that, it may also have the added benefit of being configurable so that it would just log HTTP/S connections, rather than all of them.