On this site (and its precursor), I had a survey up asking people if they would watch the show if it was on TV and if it was on pay/streaming only, and I asked their age. I've gotten over 4,000 responses over almost 2 years and it's pretty interesting.
Overall, you can see an equal amount of interest from Gen X'ers (36-50 year-olds) and Millennials (19-35 year-olds). Together they make up 77% of a potential audience. That's a pretty good demographic.
Granted, I was asking about Star Trek Uncharted, but the show the CBS press release described is similar in nature: new ship, new crew, new adventures, exploring current social issues.
Where it starts to get a bit dicey is when you ask people if they'd watch it on a pay/streaming service.
Here you can see the total responses for broadcast TV, by age group:
Another way to see this change is in the overall "would watch" responses when going from broadcast TV to pay/streaming:
That said, CBS may not care about that big of a drop because the benefits are pretty good for them. They get direct revenue for the show through subscribers, the show basically pays for itself and could be profitable from the get-go. It's also good for Star Trek because it's not subject to sponsorship, being cancelled because of bad ratings and the lack of commercials would modernize the show's dramatic format, bringing it more into line with quality shows like Game of Thrones, Downton Abbey, Daredevil, House of Cards, etc.
There is one large caveat with all this data: I only got responses from people who visited my site. So that probably means these are people who were already interested in a new Star Trek series. This doesn't really reflect what new viewers the show could bring in.
But: when you ask someone to pay to watch the show, you're pretty much limiting yourself to already-interested viewers. Unless they have a lot of other content on CBS All Access, I don't see the, getting much in the way of casual viewers checking out the new Star Trek show.
That said, as I understand CBS All Access' current model - you can watch for free with lots of ads that you can't skip, or you can pay to watch with fewer ads (but not ad-free). Only their "classic" shows are offered ad-free.
I'm not sure if this will change before Star Trek debuts on the service, and I imagine they'll want to create other exclusive content for the service, so we'll see, I suppose.