My understanding of an allusion is that is refers to a famous person, place or event. However, I have always thought they were references that carry a meaning that supports a statement or comparison.
For instance, John Adams wrote that he had 'passed the Rubicon, let the bridge be burned behind him,' and this was an allusion to Julius Caesar who crossed the Rubicon to attack Rome. The idea was that once done, there was no turning back. I agree with you that I don't know if the terms you note are allusions, per se, but understanding them definitely helps one to better understand the poem.
Wessex is found in South West England, and this is where Dummer Hodge comes from.
Karoo is found in South Africa. From 1899-1902, the British and the two Boer republics fought a war. This is probably where the drummer was practicing his art, and where he also died and was "buried."
The Bush refers to the wide open spaces (out on the 'frontier') of South Africa, also known as the "veld" or the "veldt."
The "kopje crest" refers to the top of a small hill.