I have not personally attempted what you are describing but I would be very skeptical of the possibility of your success. Assuming the Legacy Reign of Chaos CD keys are bound to your current account login, these are the keys that will allow your Battle.net account to log into the unified Warcraft III Patch 1.32 modern game client. I am doubtful that one Legacy Reign of Chaos CD key can be bound to multiple accounts. If your old CD key was not bound to your Battle.net log in, then this CD key might be “unclaimed” in that sense. If this were true, then if you bind the old CD key to your friend’s Battle.net account (meaning it is no longer yours) and then you purchase Warcraft III Reforged on your own account, then this would mean you each individually had access to the unified Warcraft III Patch 1.32 game client. As far as I know, all access to the game is based on logins in this way for the modern unified client.
If your legacy Reign of Chaos CD keys are already bound to your Battle.net account, then I would assume that these keys will not function for any other account. In that case, if you purchase Reforged then most likely doing so would unlock the HD fidelity assets for play in the game, but would not offer you additional simultaneous access to the game since it would be on the same account.
Another possible option for you might be if you start a new account, and then purchase Warcraft III on the new account. I have not investigated whether starting a new account is in violation of the Battle.net EULA, so I cannot speak for that. But I do know that if a different account purchases Warcraft III Reforged, then that other account will be able to log in to the game independently from your current account because it is a different Battle.net account.
I am not a technical support agent and I do not represent Blizzard Entertainment. I am only Retera, leaving my thoughts in case they are helpful as I pass by from the Twisting Nether.