Yes, George Takei can sway enough young people to vote because he is one of the biggest forces on the internet. He has millions of Twitter and Facebook followers and many young people look to his site to see his thoughts on the election. His politics will drive people away from Trump.
He has a large number of young supporters, many of whom believe in him because of his progressive stance on politics. He certianly has the abilty to influence people to get out and vote, but it is not clear if these voters will vote for a canidate who will enact those policies.
George Takei is, in my opinion, much younger in actions and attitude than his actual age. George is proudly married to his partner, Brad and is very open and honest about it. George is also a regular guest on Howard Stern's show and has access there to reach and convince many young voters.
George Takei is not that famous. Young people might not even know who he is. Celebrities often over emphasize that they think people will agree with them just because they are famous. Takei is much older than the young people he wants to influence. He has had different experiences than these young people, and he has no connection to them that will sway their vote.