They would turn into a huge mess unless the coder is very diligent and understand every part.
CS 'indoctrination' is not a failure of education. Surgeons have been 'indoctrinated' to know pre-op procedures.
EDIT: Let me explain my thinking a bit more - we can try to categorize software development into two categories:
1. People write messy, unorganized code that is often in the head of just one or a few folks, who are smart but unorganized and often without formal CS training. The code often has almost no tests and doesn't follow any of the standard best practices of software engineering. The code is often impossible to pass down to new people, often ending up forcing the new people to redo a large fraction of the work.
2. People write clean, modular, testable code with good unit and integration tests, a robust build framework, etc. The code is written in a manner thats super easily transferable, most devs don't even have to understand the entire codebase to start meaningfully contributing.
Obviously, the second category is the preferred category. A good SDE with a CS bg should follow (and often do follow) the second method. However, category 2 could, at least from my experience, be split into two sub-categories:
2A. The framework for both the code and the dev ecosystem was laid down by (often just one) really good engineers who think through what the problem really is and make sure that the fundamental structure and architecture of the codebase works towards solving that real world problem. This kind of code is absolute pleasure to work with and extend.
2B. The framework and the majority of the code are written by average engineers; often the first few eng hires in the company put the groundwork and make poor design choices and the engineering team that follows never wants to change anything fundamental because that's "tech debt" which the company can never afford to take a step back and look at. The average engineers have a good heart, but often their test cases never test real-world edge cases, they often don't even remember the architecture of the code they themselves wrote a few months back, and the code breaks all the time. Furthermore, the engineers would generally balk at adding any new feature because the codebase is fundamentally evolved into something that just cannot be extended without significant rework, and often they cant even see how they can rework it to add the required feature. In the end, good SDE practices and testing doesn't do shit if the person who wrote it didn't think hard enough.
Here again, 2A is the preferred method of doing dev, but unfortunately, the thoughtful smart SDEs aren't that many, and would often be found in a well-paid job in a big company. Most regular devs can't step up to that level and the end result is 2B happens.
Now the question is, which is the better of the two evils, if they are the only choices? 1 or 2B? I'd choose 1. My experience has been that while the scrappy code is unmaintenable by anyone new, at the least the guys who wrote it (assuming you can keep them long enough) will at least own up to it and make sure it keeps running, and they can at least try (and practically, generally succeed) to ship a new feature as opposed to the 2B case where often the categorical answer would be no.
It's fair to say "a program not covered by unit tests can still be good enough to get the job done" (& to suggest that this is under-appreciated), but not having sufficient test coverage significantly raises the barrier to entry for those not familiar with the code ("noobs") from contributing.
(EDIT: I wrote my comment before parent's edit)
At the end of the day, unit tests or not - you have to understand the code you are working in. This means new programmers will not deliver features as fast as those who have been working on the project for a while. They are going to need to learn the code base regardless of whether it has tests or not.