You are digging WAY too much into semantics to ignore the actual writing in the Manga. To begin with, Vivi has already made it clear she wants to sail with the Straw Hats. Next, Vivi isn't free from Alabasta, BUT, the WG is a threat to Alabasta (Sabo didn't kill Cobra, the WG did, let's be honest, and Imu had Vivi's poster). Vivi needs to ally with people who can protect Alabasta from the WG.
Next, okay, say you're right, and Vivi was using the word Nakama to mean friend, not shipmate. How does that make sense within the context of the scene, where Vivi is addressing the crew as they leave Alabasta?
Why in the hell would Vivi ask the Straw Hats if she'd be their friend still? Of course she would be. The Straw Hats wouldn't meet Vivi a few years later and act like they're not friends anymore. You and many others have openly admitted that she's an ally/friend of the Straw Hats, why would she ask if she would still be their friend?
The scene literally only makes sense if Vivi is asking if she'll still be apart of the crew.
The ENTIRE POINT OF THE SCENE with the X's on their arms, is to tell Vivi that she will always be a Straw Hat.
This thread is actually pointless if you guys can't admit Vivi already got a clear invite. Oda letting her join is one thing, but, Vivi is a Straw Hat.
Whatever you guys type on the internet won't erase the X on Luffy's arm.