Straight from Apples Website:
Use Universal Links to Enable Your App to Handle Links to Your Website
With emphasis on your website. This feature uses a combination of many things, one of which is Shared Web Credentials. Which is summarized as the following:
Accessing shared web credentials requires permission from the app, the website, and the user.
In order for access to be fulfilled an association must be created:
Add an apple-app-site-association file to your website. This file must include application identifiers for all the apps with which the site wants to share credentials, and it must be properly signed.
So in short, yes, but also no. It has to be supported by all the agencies/parties (website & app, just like handoff). In your circumstance, if twitter includes the proper certificates for universal links, (as well as Apple including entitlements) then it will redirect them as it already does.
To answer your question specifically, the technology itself is available in order to completely bypass Safari as a whole, by sending users directly to the app in question, instead of the http calls by adding specific entitlements to your own app (com.apple.developer.associated-domains), even though I understand what you meant. It's not made for Safari