No it doesn't, not in my experience anyway.
Here's one example, there are many others.
I created a route in Richmond Park in London, from the top of Sawyers Hill to the junction with Ham Gate. It includes the Strava segment The Dutch Train, and is part of the RideLondon route.
The Dutch Train segment has been ridden nearly 1.8 million times by 116,000 people making it one of the most popular anywhere in the world. I've ridden it over 800 times myself.
Any routing engine that I've tried other than Garmin (on device or Garmin connect) would take you straight from the top of Sawyers hill to Ham Gate, but Garmin takes a weird route out of the park, and back in again.
If I ride the route with re-routing, Garmin ignores the road and tries to send me onto the much less used gravel path at the side, despite being set to avoid trails.
Given how wildly popular the direct route is, what on earth is going on with the routing engine?