That’s an interesting question.
CI(Continuous Integration) defines some rules to really be considered as a CI development environment. However, it does not intrinsically define the use of an agile methodology.
But if we look at its essence, it is the continuous delivery of software, so you need to always deliver code for your IC server to do the whole process, from compiling the code to running your automated tests. This way we can realize that it is a totally incremental process, where we are always evolving and delivering a little more software.
So we can see that this process is very similar to the XP methodology (Extreme Programming), an incremental delivery that has multiple releases to verify all project premises.
If you really want to follow an IC environment you will inevitably have to follow this incremental idea, without counting, tests, software quality, etc. Things I consider to be paramount, regardless of the methodology adopted in software development.
Deploying IC in a project is not simply putting a server to do it, it’s a paradigm shift for the whole team that has to deliver software. Following your rules will make your team more productive and prone to delivering value and prevent failures.
It depends on your goal with continuous integration. What benefits do the team expect from using continuous integration? All commit continuously to the trunk (or main) and a release package to be assembled automatically is already of great help yes even if the team does not yet have for example automated tests or product Owner. Now, do continuous delivery without agile methods is very unlikely. You will need engineering and management techniques that, although you can give other names, they are already well known as "agile methodologies".
– Caffé