Might base-rate fallacy apply here?

In the UK children who use another language (in addition to English) are called EAL (English as an additional language) learners. As their English language proficiency improves they move up a five point attainment scale. The scale ranges between 'New to English' at the lowest end, and 'Fluent' at the top end. Children who are not learning English as an additional language are called 'monolingual English.'

In a recent study that compared the exam results of children at different stages on the proficiency scale found that a lower percentage of EAL leaners at each point on the scale passed the exams compared to monolingual English children, with the exception of EAL learners at point 5 (fluent). A higher percentage of EAL learners who were classified as fluent passed the exam than the percentage of monolingual English children who did.

It is tempting to conclude that children who are EAL leaners and who are fluent in English stand a higher chance of passing these exams than their monolingual English peers.

The numbers break down like so:
Total number of children whose exam results were analysed = 2829
Number of monolingual English children = 1381, pass rate 71%
Number of 'fluent' EAL children = 487, pass rate 85%
Number of 'not fluent' EAL children = 961, pass rate 55%

Is there anything fallacious going on here, or is the conclusion that you stand a better chance of passing your exam if you are an EAL learner who is fluent in English than if you are a monolingual English speaker a sound one?

Nothing fallacious going on. Because we are talking in percentages, and the sample sizes are sufficient in each category, the conclusion makes sense. Based on the results (assuming they are correct and the methodology is not flawed), students who are fluent EAL will have the best chance at passing. This conclusion is derived from purely statistical information (with the base rate fallacy, statistical information is ignored or minimized over other information).

{date-time stamp}Friday, Nov 10, 2017 06:43 AM{/date-time stamp}

I guess the next thing to think about is whether this relationship is causal or not. That is to say, does being fluent cause children to pass exams, or is being fluent and passing exams the consequence of something else.

This appears to be a correlational study . This means that this study only demonstrated a correlation (a relationship), not causality. It doesn't mean, however, that there is no causal relationship; just that one has yet to be established. To establish such a relationship, a controlled experiment would need to be done where only variable that changes is the fluency. That would be quite challenging to do (if not practically impossible).

It doesn't seem like anything fallacious is occurring. Assuming the sample size is large enough, and that the procedures used to obtain the results were honest, it's reasonable to conclude that those individuals are more likely to pass because that's what the results directly show.

You're not ignoring any information relevant to your conclusion.