I'm reminded of the old saying: "you don't have to be crazy to work here, but it helps".
The short answer is that hands-on coding experience isn't a requisite of a good software PM, but it is usually preferred. What is critical to being an able PM is understanding the development process (whatever methodology is used), and trusting that the developers are willing and able to do their job. The development experience gives hands-on knowledge of that process, therefore it helps. PMs who work their way up the ladder in a company additionally know the corporate culture (and the codebase), and have a rapport with the other long-serving members of the dev team, which is why IMO the best PMs are promoted from within instead of being brought in from outside. If someone outside the company can manage the team better than someone from inside can, things are VERY wrong.
One thing I mentioned is a rapport between the PM and dev team. This is both at an interpersonal and a technical level. The key here is communication; the devs must feel they can bring issues, both technical and interpersonal, to the PM, and the PM must understand the dev team members when they describe a problem.
As to the specific nature of your question, an estimate is exactly that; an educated guess as to a quantity (as opposed to a hypothesis, which is a more general prediction of the outcome of a future event). The manager will usually either mathematically or intuitively apply some modifier, based on your recent estimates versus actual timelines. Agile builds this into the estimation process; the client intuitively estimates the complexity of the requirements, then the devs do the same, and then the devs actually go out and develop the solution, giving the manager data points to calculate a ratio of requirements points to dev points, and dev points to man-hour requirements.
In short, a manager will only take your estimate at face value in one of three scenarios:
- You've been pretty accurate with your estimates of similar tasks in the past.
- He's under pressure to deliver, and your estimate is better than he thought.
- He's looking for a reason to fire you.
If it's that last situation, there will be many other clues around the workplace that maybe you should get the hell out.