The Purpose of CI for Project Management
While the question as originally posed isn't really an ideal fit for this site (e.g. it's more about development practice than about managing projects) it is nevertheless a useful question when properly framed.
The Value of Automation to a Project Manager
From a project management perspective, real-world projects typically require (among other things):
- Validation against requirements.
- Regression testing of existing features.
- Acceptance testing of new features.
Continuous integration fulfills this role in an automated way, meaning that it doesn't have to be explicitly managed. This often creates efficiencies for the project over time. From the perspective of a project manager, it may also mean fewer bugs will go unnoticed long enough to impact the overall project estimates or release dates negatively.
Can you do this without CI? Sure. But if you have even two developers on your team, then there will also be integration work (you did plan on feature integration in your project plan, didn't you?) that can and should be automated.
From a project management perspective, frequent integration testing means fewer integration death marches at the end of a project. In my experience, any big project without automated integration testing has a strong tendency to blow its schedule because the effort and complexity of manual integration testing grows over time--and if it's left until the end of the project, you won't be able to accurately estimate the size of the effort involved.
Another purpose of CI is as an information dashboard. A good CI system with both effective tests and sufficient code coverage will communicate the status of the project quickly to anyone who's interested. CI won't tell anyone what features are available in the code base, but a green dashboard will certainly tell stakeholders that whatever features are present and tested are ready to ship.
Of course, just like any other tool or project management technique, the CI dashboard can be abused. For example, taking out failing tests just to "green up" the dashboard violates the principles of effective communication and transparency that all project managers should strive for, but I've seen it happen for political reasons and through organizational dysfunction.
As a project manager, communication of project status is extremely important. If some of that communication can be automated, that represents a project efficiency that usually adds measurable value.
While CI is useful from a technical point of view, it can also be useful to create efficiencies and enhance communication within a project management framework. Unless your project is truly trivial, avoiding the overhead of automating tests is usually a false economy.