Allright seems i'm the only one with the correct information here.
Mechanically speaking, all c'thun buffs are applied to your hero. Hence, if you steal his c'thun, it will have your c'thun buffs (much like doomcaller reviving c'thun).
This was mentioned by ben brode (not in last week's stream, in another video. The winter champ i believe), so it should be accurate.