Hickory: Incorrect information. You *cannot* have Drizzt's scimitar with you in BG2 when you meet him.
bushwhacker2k: Elaborate, please.
Here's a more technical explanation:
At the start of BG2, before you gain control, there is a scripted event that removes every item from your inventory. This, in particular, means you don't get to keep that scimitar.
Now, if you're not playing the EE, it is possible to keep that scimitar by accessing your inventory before the scripted event occurs (you need to be quick here) and then dropping the scimitar on the ground. Or, of course, you could just cheat the scimitar into your inventory with the cheat console. However, the developers were obviously not expecting the player to do this, and therefore probably did not account for this possibility.
If you somehow have the scimitar when you meet Drizzt in BG2, the game will most likely be oblivious to that fact (I would be surprised if not). Drizzt won't say anything different, and he will still have the scimitar, meaning there will be a duplicate of that item. Now, killing Drizzt in BG2 will result in someone coming to take the equipment you took from him; I do not know if he'll take that scimitar you glitched or cheated into your inventory.
Also, from what I've read, in at least one of the games, if you name your character "Drizzt" the real Drizzt will accuse you of stealing his name (or something to that effect), and you will get different dialog. (I don't know if anything else changes here.)
You might be able to bypass the event by importing directly into Throne of Bhaal, but doing so will also skip the Drizzt encounter, so you won't encounter him while carrying his scimitar if you do this.