This question gets frequently asked, not only about this route, but about other routes (most often about the TransAmerica Trail). The answer is always that nobody knows. The ACA knows how many maps they sell, but that's a poor correlation to the number of riders, since maps are sold to people that never ride the route, people start and never finish, and a single map set can be used by a whole group. There's no sign-in book at the start, nor finish book at the end. The ACA does count the number of people who stop at the HQ in Missoula, but it's likely that count misses a lot of people who never go there, show up when they are closed, or don't bother to sign in. And the ACA encourages people to log their tours on this site, but I'll bet that most people don't. Then there are questions about what qualified as riding a route. Does that mean every mile? How do you count people who rode part of the route?
People love to make guesses, usually based on how many people they saw when they rode the route, or how many people they counted in the log book at Cooky's Cafe, or something else, but these guesses are very rough.
There's an opportunity for you here. Devise a system to get an accurate count. Get volunteers to take shifts at the Yorktown Victory Monument and the Columbia River Maritime Museum for all the daylight hours for the year, who collect names and then contact them later to see how far they got.
It would be a big job. Too big.