What would be the role of the manager?
First case: team and project manager
If he would handle the team and organize how the project is done, then indeed, without technical background, such manager might become a real treat which will lead to project failure. For this task, you need a person who understands:
How developers are working and thinking by comparison to other jobs:
- What are their motivations?
- Why new features should be in production as soon as possible?
- Why comparing the raw productivity of two developers is so difficult?
- What are the real skills (such as communication skills) required from a developer?
How project is managed, especially:
- What is technical debt and why should it be taken in account?
- What are the techniques used for risk mitigation in software development projects?
- What iterative development brings to the project?
- Why tasks, such as refactoring, which don't deliver immediately visible features are often much more important than shipping just another feature?
- Why it's ok to go back and forth, instead of moving towards a goal?
- Why “solve this bug ASAP”/“deliver this feature ASAP” is crazy in practically every situation?
- What is the difference between a prototype and a solid production code?
What are the points which should be in focus from the beginning. While a team of developers with minimum experience will not forget to do unit tests or regular refactoring, they may be too focused on their own job.
Sometimes, they forget about UX, security, deployment or end-user documentation, simply because it's not their job, and when the product appears unusable, insecure, a nightmare for system administrators or lacking basic documentation, it's often too late.
It belongs to the manager to determine all the tasks required for a successful project, and to find the resources needed for their accomplishment. Having a bunch of programmers is not enough.
Second case: an intermediary between IT and non-technical world
If, instead, his task is to ensure good relations between the technical stuff and non-technical stakeholders, then a person who studied management, but has only light understanding of technical stuff may be ok.
Even then, try to pick a person who understands the specificity of software development and who have already a professional experience of several project failures: it would be a disaster to hire someone who would treat developers as “the guys who play with computers and are never able to get the stuff done”.
Let's consider the points you included in your edit:
Create tasks for developers
What does that mean? Do you mean user stories? As is, there is no way to answer without knowing how those tasks are created in your team.
Monitor that our ticket workflow is respected
If it's not, what would happen?
The good answer is: “Retrospective will be used to identify what went wrong, in order to solve the previous issues and adjust the schedules to the speed of the team.” This requires technical background.
The bad answer is: “The project manager would scream to team members, and tell that either they start programming faster, or somebody among them will be fired.” This doesn't require any specific skill.
Warn developers is they cross estimated work time
See the previous points.
Manage weekly finance timesheets
No IT-related skills required here. But the manager should be aware of the specificity of software development, including the fact that it's often impossible to predict how much a feature would cost to implement.
Help client and reply to his questions
Questions such as “When do we have our next meeting?” don't require technical background. Questions such as “Is it possible to still use the synchronization mechanism we talked about the last week in a context of frequent connection loss?” requires to understand the inner workings of the project.
Set meetings between client and developers (internet meetings)
No technical skills needed here.