Currently my D6 site relies heavily on Memcache and apc to deal with high load of a busy social site. The memcache is on a single webserver and the database on another server.
No, it unfortunately does not.
Redis and Authcache are two completely separate systems/concepts, one cannot be used in place of the other.
Redis is a key/value store, primarily used in Drupal as a cache backend.
Authcache provides the mechanism to store/serve cached pages to authenticated and un-authenticated users alike. It uses a cache backend such as Redis for storage, but it is not itself a cache backend.
On the flip-side, Redis is a dumb key/value store, that has no concept of authenticated/unauthenticated users. It cannot be used to replace the functionality provided by Authcache, which is necessary to (amongst other things) build appropriate cache ids based on the user's authentication status, and persist rendered pages, or parts of pages.
The How does Redis compare to Authcache? thread you linked to, in the (now deleted) comments, puts it nice and succinctly:
the question isn't about Authcache, it's really "Memcached vs Redis".
Which I agree with, and is actually what the original revision of your question was asking. So it kind of all makes sense.
Just in case you're basing the question on this obsolete bit of information from the Pantheon docs:
"Redis adds caching for authenticated users, which can greatly alleviate request bottlenecks..."
Please note that advice has now been removed as it was misleading. Redis does not provide caching for authenticated users in and of itself, but it can be a part of that process if Authcache is enabled over the top.
BTW I should add that I wish Redis did make Authcache redundant - I'm right in the middle of converting a large social site to use authcache, and it's not an easy process. The above 'knowledge' has been gathered through extensive reading and back-and-forth with the Pantheon engineers.
Also, slightly off topic but possibly relevant to your decision making process: the Pantheon engineers recommend the authcache approach over something like ESI, because of the increase in the number of app-server bootstraps. So if you're looking for an advanced caching solution for auth'd users, authcache is probably the best way to go.