Q: How big a part did violence pay in moving ANC forward?
A: These things are always difficult to gauge, but it's worth noting that pretty much every means of non-violent struggle were exhausted over many years. In my view Nelson Mandela was justified in shifting gears in the early 60s and founding the Spear of the Nation to initiate a campaign of sabotage. That's not to say every single action was justified, and indeed Mandela didn't simply believe that the resistance was to be fought by all means available. He was an opponent of car-bombing for example, precisely because it would degrade the movement. It's also the case that Mandela was very careful to select government targets, as well as industrial and agricultural targets for sabotage. So this wasn't indiscriminate civilian bloodshed for the most part. Then we have to put the struggle in its regional context.
The decolonization of Africa was still underway when Mandela undertook the new approach, but the liberation of Spanish and Portuguese colonies was stalled until the Fascist regimes began to collapse in the late 60s and early 70s. The primary force of counter-revolution in the region was Apartheid South Africa and it quickly moved to try and prevent its neighbours from achieving independence. The CIA was heavily involved of course. South Africa occupied Namibia and intervened in Angola and Mozambique, as well as organising bombing raids, coups and death squads in a lot of other places. We're talking 1.5 million dead plus $60 billion in damage from 1980 to 1988. Cuba pledged a great deal of support for the rebels in Angola, Namibia as well as the ANC. In fact, the ANC along with the MPLA and SWAPO fought alongside one another at Cuito Cuanavale in what Nelson Mandela called "a turning point for the liberation of our continent and my people."
I don't claim expert knowledge on this. My South African friends will probably have a lot to add on this. I would stress the demands of historical conditions and how quickly those demands can change. Gandhi's approach worked because the British Empire was crippled. You couldn't say that about the South African state in 1961.
Afterthoughts: Eventually the South African state was effectively crippled through the boycott campaigns and the international sanctions imposed on the country as opposition gradually became the predominant position in the world. Once the US had given up on Apartheid the South African regime had no choice but to dismantle the system of white supremacy. The next best scenario for the Afrikaner elite in South Africa was a compromise where the black masses would be given suffrage, while overwhelming economic power would remain in the hands of the white minority. The business class realised this by the late 1980s and began meeting secretly with Oliver Tambo and others in places like Zambia. It took the political class a bit longer to reach the same conclusion. Once free Nelson Mandela and the ANC negotiated away the possibility of economic justice, possibly out of fear of what the white generals might do if the ANC opts for significant social and economic reform. In this way we might understand Nelson Mandela as a transitional figure in an unfinished revolution.