The title begs the question of why it should be "yes". American sports is littered with examples of why "you can never go home again". Even Joe Gibbs couldn't replicate his success, and Billy Martin got four more cracks at the Yankees job without result after the one Series title. Those are among the more successful of the retreads.
Dalglish lifted a League Cup, but it would be quite the stretch to suggest that his second run was on a par with his first. Mourinho won nothing on his second go-round at Chelsea. Ancelotti isn't setting the world on fire at Madrid.
The evidence suggests that it just doesn't work, and it's fairly overwhelming. That's why it's always "no", and that's without even addressing Moyes' specific tactical limitations against the top managers and clubs over the years.