Would Magnus Carlsen be unable to play chess if he had no words for it? This old post suggests some people don't have mental imagery at all. If that's true, these people would probably make some interesting claims about thinking.

Or could he not even be able to understand, say, that a patient was having a heart attack if he did not have the words for it?

I can visualize a "heart attack" in my mind with all the relevant steps involved, no words needed. People (and animals) understand other kinds of phenomenoms they don't have words for, so I would deduce that it applies to this situation also. Symbols are needed for understanding phenomenoms you're not directly experiencing, but they don't have to be words.

So do you have an argument for or against the need for an advanced or specialised vocabulary to be rational? Is it a question that's too vague, or with too variable an answer?

Specialized vocabulary usually makes thinking and communication more effective by allowing shorthand for complex concepts. This applies to many kinds of thinking, most of it not necessarily rational. You'd probably find correlation, but good luck with the causation part.