The peace and literature prizes do, because those subjects are defined by their contemporary relevance. The peace prize is frequently controversial, and I'd say that it's best suited to bring attention to somebody who isn't already famous.
Most of the Peace prizes that people do widely agree on are already "influencers", and have been since the beginning. Their influence usually requires physical presence and a lot of effort, but I see no reason it couldn't go to somebody who was effective just by being on social media.
A literature prize could conceivably be given for a social media account, but it seems unlikely to be soon. Even a controversial choice like Bob Dylan got it for a lifetime of highly enduring work.
I'm more interested in knowing what an influencer will need to do to get the price.