God, no. That's just begging for abuse and would affect EVERYTHING from how new accounts would clear content in hours to even the in game economy. Not to mention its effects to company profits and its subsequent effects to the longevity of the game.
Like @Shadowstrike said, this would cause so many problems. The gifting event has cause so many players to complain that they got rob and this won't be any different. I will give you my Hercules for your Doom, you send it first and I will send it afterwards. Also everyone will create so many accounts just to trade with themselves to get the champ they can't seem to get on their account. This would hurt Kabam's pocket book so that's a no go for sure.
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TLDR; NO!