I should begin by warning you that I am not noted for having humble opinions.
I assume the Moodle admin is trying to explain why they don't wish to install CodeRunner on their Moodle system. The logic being: "If we install it, people will use it, and our system will overload". Which is a true statement for any under-resourced computer service.
That said, installing CodeRunner does add load and the Moodle administrators are right to consider the impacts of that load. But I'm curious about the factor of six mentioned for CodeRunner user load versus "standard user" load.
Processing of a single answer to a CodeRunner question goes through the standard Moodle question processing and grading infrastructure except that the actual grading is passed off to the sandbox server, called "Jobe". Except on Jobe, processing doesn't involve any more database or disk accesses, which are often the bottleneck for Moodle systems. Nearly all the extra load of processing a CodeRunner submission is taken up by the Jobe server. So in terms of the Moodle system itself, I doubt that CodeRunner adds significantly more load than any other Moodle question type for processing a single submission of a student answer.
The resourcing of the Jobe server (or servers) is a different matter. Certainly it needs to be thought through carefully, particularly if you're running CodeRunner-based tests or exams. The actual cost of grading a question answer depends greatly on the language and the type of question. There is at least a factor of 10 difference between the cost of grading a small C or Python program compared to a similar-sized Java program, for example.
There's no database on the Jobe server and the cost of grading a submission is largely in CPU time, at least for C and Python. If you're running tests or exams you need to measure the time taken to grade a single submission, multiply that by the number of questions in the exam, the likely number of (re)submissions per question and the number of students. Toss in another factor of (say, wild guess) 5 for load fluctuations, and make sure you have the required Jobe CPU capacity. For many years we ran tests and exams with classes of several hundred students in an introductory Python course on a single 8-core Jobe server with around 8GB RAM. But after one unpleasant occasion when we overloaded Jobe, we now have a Jobe reverse proxy server that distributes jobs to a pool of Jobe servers. Alternatively you can configure CodeRunner with a list of Jobe servers, separated by semicolons.
I should also mention that in our department we run our own Moodle server for (mainly) CodeRunner-based courses. The main University Moodle server also has CodeRunner installed but is configured to use our Jobe subsystem.
If the Jobe service becomes overloaded during a test or exam, it can indeed bring the main Moodle server down, because the queue of jobs awaiting a Jobe server run can hit a preset limit, blocking other users. The CodeRunner documentation does say "However, if CodeRunner-based quizzes are to be used for tests and final exams, a separate Moodle server is recommended, both for load reasons and so that various Moodle communication facilities, like chat and messaging, can be turned off without impacting other classes."
So to summarise, your Moodle admin is right to consider load implications of installing CodeRunner. But rather than ruling it out because of resourcing, they should be considering what resources they would need to support it properly, given the expected usage. If your Moodle admin staff tell you it's not possible, ask them how it is that there are nearly four thousand Moodle servers running CodeRunner worldwide.