I don't think it's possible as there isn't a SC2Armory or anything for it, yet. I do like the idea of adding it to profiles, though, despite this mostly being a Custom Map centric site.
Currently Working On: My Overwatch addiction.
http://beta-us.battle.net/sc2/en/forum/This is the new Blizzard Official Sc2/Esports website. By clicking any members portrait in the forums etc.. it shows you their profile page, which looks identical to viewing profiles while on SC2. It shows their league, points, win loss ratios, achievements, match history etc... So yea its possible to sync accounts to profiles, but only blizzard has done that now.
None.
Oh very cool, didn't realize that. Thanks!
Currently Working On: My Overwatch addiction.