It's the Orange Free State (singular), not "Orange Free States."
There were two independent Boer states in the late nineteenth century: The Orange Free State and its northern neighbor, the South African Republic (a.k.a. the Transvaal). Of the two, the Orange Free State was probably the more successful and stable.
There are a couple of reasons why this is completely implausible:
1) The sheer distances involved. The US would not be in any position to support the efforts of its filibusters (who could probably not do much to help the Boers, anyhow).
2) The US wouldn't want to piss off the British. Even the Germans didn't want to make the British mad by helping out the Boers. (BTW, if you want foreign intervention, that is a much better POD: have the Germans come crashing into the party during the Second Boer War around the turn of the century.)
3) Lastly, the Orange Free State was completely landlocked (with the exception of a couple of rivers, obviously). All the ports around it were controlled by the British, who weren't about to let anyone enter the area who were looking to help the Boers.