The South African colonies were well on the way to uniting with or without the war- the economic centre of gravity had decisively shifted to Johannesburg. The Cape and Natal colonies were absolutely dependent on the customs revenue gained by the shipping of Transvaal gold on their railways to their ports.
The historian Ian Phimister argues that the British drive to war in 1899 should be understood as an attempt to take control of a process of confederation that was already underway and ensure that it took place under the auspices of the Empire.
For example, in 1896 the Colonial Undersecretary Lord Selborne wrote a memorandum warning that:
"The key to the future of South Africa is in the Transvaal… the richest spot on earth… [it] is going to be the natural capital state and centre of South African commercial, social and political life…. [the loss of rail revenues would drive the Cape and Natal] to the verge of bankruptcy, so dependent are they upon their rail revenue. It needs no words to prove what a powerful use could be made of this instrument in squeezing the British South African Colonies into joining a United South African Republic."
He was right. By 1898 the ZAR had completed its own rail link to the Portuguese coast- and the Cape's profit from rail revenues dropped from 349,000 pounds to 1896 (at the time of Selborne's memorandum) to almost nothing in 1898.
This brings us to the major point:
For the Boer Republics to be in any position to unify northern South Africa- and to do so once Rhodesia exists- the gold rush has to happen. However, once the gold rush happens, those republics will steadily lose their Boer character.
By the time of the war, the Uitlanders (foreign-born residents, chiefly British) outnumbered the Boers. One of the reasons Paul Kruger went to war is that he knew that any political concessions- the granting of the vote, for example- would immediately end the agrarian, ultra-Calvinist character of the Transvaal.
But: for all the British talk about Uitlander rights before the outbreak of the war, they didn't necessarily want those rights to be granted by anyone other than the British.
Because once the Uitlanders are in control of the state, they don't need the Empire's protection any more- and as Selborne put it, “this country so powerful in its future wealth and population must be a British Republic if it is not a British Colony… [and] would assuredly attract to itself all the British Colonies in South Africa.”
The Boers could have protected the character of their states by winning a short war with the British and then expelling the Uitlanders. In the process, however, they would have utterly crippled their economy and provided the British with a perfect casus belli for a third war, one that this time they would actually have prepared for.
TL,DR: By the time Rhodesia is established, the South African gold rush is underway. Once the gold rush has happened, South Africa is on a ticking clock to some kind of unification- and it almost certainly won't be by the Boers.