Not sure if it has been posted yet, so apologies in advance if it was. (Checked the OP and everything)
Future Sight on the main server play.pokemonshowdown does not seem to get a Choice Specs boost.
http://replay.pokemonshowdown.com/uu-256932843 (turn 8) (Damage Calc -
http://puu.sh/jv4qJ.png shown with Psychic's power set to 120 to mimic Future Sight)
http://replay.pokemonshowdown.com/uu-256931419 (turn 7) (Damage Calc -
http://puu.sh/jv4x4.png)
http://replay.pokemonshowdown.com/welivin-ou-16740 (turn 6) (not Mega Bro, I named it that to maybe fool people) (Damage Calc -
http://puu.sh/jv4zk.png)
However, very interestingly enough, on other certain servers for example Smogtours, Future Sight does get the Specs boost as seen in this test match
http://replay.pokemonshowdown.com/smogtours-uu-80894 (see turns 3, 6, and 15 to see damage difference after tricking away Specs)
Really not sure what the actual cartridge mechanics are, as pokemon websites such as bulbapedia/serebii etc never mentioned Specs Future Sight mechanics
Doom Desire might be worth checking out as well
I believe that those two important servers should have the same mechanics at the very least