Yes, so long as you are connected with Facebook.

In Angry Birds Friends, your in-game friends are determined by your Facebook connections. If your game is linked to Facebook, you'll see and be able to play with your Facebook friends who also play the game.

Therefore, linking your Facebook progress to Red's Club on the web version will still allow you to play with those same Facebook friends.

If your Facebook progress is linked with the game & Red's Club correctly, your "settings" page should look like the image below. Note that the Red's Club connection status is "Linked" and the Facebook connection status shows that you are already connected with Facebook. 

For any difficulties linking your Facebook progress to AB Friends WEB or if your Facebook friends aren't appearing, please contact player support for assistance!