This led to tens of thousands of civilian deaths in the camps - partly due to disease, partly due to starvation (the Boers had been attacking supply trains).

This is a bit of a misunderstanding. By far the biggest cause of problems in the camps was the unpreparedness of the British administrators, who were not ready to deal with the enormous strain of the scorched earth policy. The problems did not originate with Boers attacking supply trains (which they weren't actually that good at, especially once the blockhouses and armoured trains were put into practise), it was the British soldiers burning down the farms. It's a bit difficult to farm food if many of the farms have been razed, and a bit difficult to manage interned or displaced people if the army adopts a scorched earth policy with a complete lack of care for the burden that places onto camps. The problems of the British concentration camps were almost entirely of their own making, which I wrote about here in response to a British politician defending the camps.

Was this strategy effective in defeating the Boers, or was it inconsequential?

It's hard to tell, simply because the British threw every idea they had at the war. This makes it difficult to pick a single strategy and judge its individual effectiveness among a maelstrom of factors. That being said, there is evidence that camps demoralised some Boers but emboldened others, and was therefore not of significant military value overall. It also placed enormous financial and logistical pressure on the British administrators, under which the camps buckled, resulting in a ghastly number of deaths. This probably wasn't worth it even putting aside all moral decency, and it may be worth noting that Lord Kitchener ordered soldiers to stop bringing people to the camps at the end of 1901 (just as British administrators were finally getting the hang of running them), but whether that was because he thought it wasn't really achieving anything or because the camps were causing a severe backlash both internationally and in the British government is difficult to discern. Perhaps it was both. Here we run into the problem of attempting to view the camps purely militarily, since public opinion can absolutely have an impact on the course of a war. The Second Boer War was an extremely complex campaign so asking anything along the lines of "Did [insert specific, individual policy here] win the war?" is a bit futile. The wider campaign of psychological pressure used by the British can be analysed however, and read about here in an old answer by u/khosikulu.