Per Manolov, "No web browsers involved anymore" in Battlefield 1. It remains to be seen if that pertains to just the launching process of the game, or Battelog in its entirety (stats, loadout, friends, etc.).
I for one, would like to see it stay around as an optional and convenient secondary tool, while still having all capabilities at your fingertips in-game. Time shall tell. Westie is claiming a new desktop launcher wil lbe implemented and that it will be pushed to Battlefield 4 and Battlefield: Hardline as well. Stay tuned for developments - as new features will be emerging prior to Battlefield 1 release (such as the new squad system / UI which is now in Beta mode for certain BF4 players) - this may be one of them. What are your thoughts on Battlelog?