It would, but depending on the dictionary there might not be much, if any, context about the game.
You could get a simple “Concker(n), colloquial name for the seeds of the horse chestnut tree” or “Conckers(n), traditional game played mainly in the British Isles with seeds of the horse chestnut tree” – a concise definition of the what without any detail of the game or its cultural significance (it was a big thing for a short time each year back when I was of school age, and had been for generations).
“when I was very young and read the Hitchhikers Guide for the first time” suggests this was quite some time ago, so further lookups might have required a physical trip to a library, rather than just clicking a link or throwing a term at an online search engine.
This was actually before I started elementary school. Once I did start school I recall looking it up and not finding anything in the dictionaries to which I had access in a midwestern small town - school, local public library etc. I assume if I had checked the big pedestal dictionary in the public library I would have found it. But being very young I didn't think to. When I reread it a few years later (still very young) I just got the context that it was a kids game and moved on. I wasn't ever so desperate to know that I went avidly looking for an answer. But when my aunt went to London I did think to ask so I got an answer.
I was curious, and looked in my paperback Merriam Webster american english dictionary that I used through out school and received about the time I first read HHGTTG. Conker is not present.
The big honking dictionary on a pedestal at the high school library probably would have had it, and if that was not enlightening then the library in the closest city that we visited monthly would have good encyclopedias that probably would have described it. But I don't remember the conkers reference catching my imagination, and probably wrote it off as a silly made-up sci-fi word.
You'd need an encyclopedia to have any real chance of understanding what kind of game it is, a dictionary typically only gives very small amounts of context.
