Whatever the case maybe, he already has this public reputation that whatever thing he shows interest on, millions of people will follow same because he has them as many as possible being his followers, so there's this mentality of social media influence that works along for doge, let's even forget now about the Elon ownership or not, if any public figure shows interest on something, it will make the thing surge high and part of it is happening to how we see in doge.
That's correct, being a reputable and a successful business man, he has indirectly draw the attention of the public and create for himself, genuine fan that are ready to follow up whatever he does. So definitely the more he talk about doge coin the more his fan will get more interested, and that might trigger a small spike in price. Though most persons still find this act irritating as they complain of how he is using his influence to manipulate the coin tossing it to and fro.