Just because you have an app, it doesn't necessarily mean that many fewer users will use your website. Users that come from search engines would still get directed to your web site, for example. Personally I prefer to use responsive websites compared to apps on my phone. Apps generally ask for too many permissions and annoy me with notifications and updates. I almost always use the website if it has a nice responsive design. I can't speak for most users, but I find apps to be the less comfortable experience. I doubt that many users that would normally be using the website will want to use the app instead. The draw of creating an app is usually to try to get additional users through app promotion channels such as the app store.
Even if your app does cannibalize site traffic, Google doesn't use the amount of traffic your website gets as a ranking signal.
- They don't have access to that data for all websites.
- It would be a poor signal because of the feedback loop effect. Once Google sent traffic to the site by ranking the site higher, using traffic as a ranking signal would want to boost the site even higher. Google sends the majority of traffic on the web, so the loop effect wouldn't be small.
- It would mean that rankings could be bought by buying traffic. Google wants to avoid situations that allow rankings to be bought.
There are tons of apps that duplicate the functionality of a website, including one from StackExchange. If apps cause ranking problems I doubt that apps that mimic websites would be very common.