No, Vettel doesn't have charisma. But I think no driver on the current grid has. Maybe only Kimi, but it's hard to judge if it's charisma or just his unfazedness. Webber can be also percieved as charismatic, but I think that's just because there is currently no competition in that field.
I think that since drivers are getting into F1 so young(and are part of various programs before they enter), they tend to be moulded by the teams and behave in accordance with the team expectations and demands (as in, giving insincere and boring cliche comments for the media and racing interviews, and so on). If we judge by that, they cannot be perceived as leaders (as in one facctor of being charismatic). As I've said, only Kimi seems to have such genuine stance, but with him it's more "just let me be so I can play with my toys" than charisma.
My case in point: an example of father and son in F1 - Keke and Nico. Nico is currently being a mercedes errand boy, while Keke was much more charismatic. Not the most charismatic F1 diver ever, but above current F1 field.
And before someone sas that Vettel didn't act in accordance with teams demands in the Multi21 case, and therefore showed charisma - dead wrong. Defiance isn't in itself indicator of charisma. If anything, that evend burried the little charisma Vettel had. Why? Because, if anything, people don't apprechiate insincere, two faced behaviour. If Vettel said on the radio "No, tell the Aussie I'm gonna give him a run for his money", and has beaten him on track, he would be perceived as much more charismatic than he is now.