We have extensive records on what happens after volcano eruptions. So we know what happens. Because it has happened many times before.
And yes, if the alternative is an extinction-level event, for example a runaway greenhouse effect turning the earth into Venus, then stomping on the brakes with anything whatsoever is a perfectly valid proposal. And doing something comparable to a volcano doesn't come close to "anything whatsoever", because, as I said, we have records of how this plays out, and it happens all the time anyway.
And if you are saying that this isn't an acceptable way to proceed, which is a perfectly valid position, then very obviously the alternative cannot be an extinction-level event such as a runaway greenhouse effect that will turn Earth into Venus.
What you cannot have is have it both ways. Which is where a lot of people currently seem to be positioned. As in "we are literally destroying the planet AND geo-engineering is unacceptable". Nope. Pick one.
Furthermore, injecting SO2 into the atmosphere is easy enough that it is well in reach of pretty much every state actor whose population is going to be most severely affected by climate change, in particular "wet-bulb events". So the question of whether we want this to happen or not really isn't relevant. It almost certainly will happen.