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As nodes are in competition with each other over who mines the next block first, does geography play a role in that competition? Would a 100 KH/sec mining pool located in, for example, Plettenberg Bay, South Africa have a more difficult time winning a block reward than a 100 KH/sec mining pool located in New York City?

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What matters is where the last block was found, and this is due to latency. So if the last block was found on a pool server in new york, another pool server located in new york will be notified of the new block a lot faster than a pool located in france.

Granted, we're talking on the scale of milliseconds here, but if you do the napkin calculations of a 1 megahash per second pool, a 100 msec delay between a new york server and a server in france means that the new york server can perform 100,000 hashes before the pool in france is even aware of the new block.

Ultimately, these minuscule advantages are for edge cases when a pool gets lucky and finds a new block very quickly. More often than not, multiple seconds have passed before a new block has been discovered and these latencies do not matter, so ultimately it does not matter where a node is geographically.

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I fully agree with Ginger Ale's answer, though I think - in a way - it only partially answered the question. Ginger Ale correctly pointed out a miner is at a disadvantage if the most recent block was mined at a geographically distant location. Let's ignore that initial geographical bias for a moment, even though it still would make a different in real life. Actually, in my answer, the geographical bias is irrelevant.

Using the example in the question, let's say that a block is mined simultaneously in both NY and SA. Let's also assume for this discussion that average internet speeds within and into/out of North America, East Asia, and Europe are twice as fast as speeds for Africa.

In this scenario, news of the new NY block will reach North America, Europe, and East Asia before news of the SA block. News of the new SA block may only reach Africa and Southwest Asia in the same period of time. Once the blocks have propagated, each blockchain will be the same length, each with an equal amount of work performed on it (at least for this argument, we'll assume PoW is exactly the same).

Ever since the moment when the NY and SA blocks were mined, on average (even assuming an evenly-distributed miner population, which is likely not true), more hashing power has been working on finding the next block on the NY blockchain, due to the previous block reaching those miners first. Therefore, there is a greater chance that a block will be found first on the NY blockchain.

Since the NY blockchain is more likely to have the next block, and therefore next block after that, it will eventually clearly demonstrate to the network to have a larger proof-of-work. When that happens, the SA network will reorganize around the longer NY blockchain, which will leave the orphaned block on the SA blockchain, and which will accept the NY block as the "true" block that was mined. In this way, miners that have a higher proximity to other network hashrate are at a slight advantage. This is one example of a reason that block-size is said to be relevant to the success of a cryptocurrency.

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