Would a volcanic winter trigger an oceanic "spring"? There is large amounts of observations supporting the effects of volcanic eruptions on climate: A long term subtle warming effect due to $\small\mathsf{CO_2}$ and a short term, but more intense cooling effect due ash and sulfur gases.
There is also much evidence supporting long and dramatic volcano triggered 
 cooling events dubbed "volcanic winters", like the one after the 1815 eruption of Mount Tambora, or the Toba catastrophe 74,000 years ago, perhaps lasting up to a decade.

For more recent volcanic eruptions, there is evidence of algae blooms produced by the input of nutrients from volcanic eruptions (1, 2). Perhaps an expected outcome given that the ecosystems at the surface of the ocean are nutrient limited, therefore wasting most of the available energy due to the lack of iron, nitrogen and phosphorous mainly.

For all the above, I would be inclined to think that a large volcanic winter would encompass a period of prosperity for oceanic life. Where a small decrease in solar irradiation is more than compensated by a large increase in nutrients availability. However, I haven't hear of evidence of such oceanic boom.

Are there observations suggesting or disproving such oceanic booms during volcanic winter events?

PS: I started pondering this question while thinking about this article, on which they found that a coastal community in South Africa didn't seem to have been affected by the Toba "catastrophe", but on the contrary, they seem to have benefited from it.
I can't answer the question in detail but maybe take some of the tension, addressing the so called bottleneck hypothesis.

It was never really supported by archaeology, the mentioned article just adds to the evidence that human variety didn't suffer that greatly from the Toba eruption as the bottleneck hypothesis might suggest and that there was no decade long volcanic winter.

Example from lake Malawi after the eruption:
https://www.sciencedirect.com/science/article/abs/pii/S0047248417302750?via%3Dihub

Southe Africa:
https://www.nature.com/articles/nature25967

India:
https://science.sciencemag.org/content/317/5834/114

And to my knowledge no extinction signal in Neandertal population (they were few anyway) during oxygen isotope stage 4 in Europe.

Some think that it is time to put the bottleneck hypothesis ad acta. 

There is evidence that eruptions "fuel" phytoplankton, but not necessarily connected to volcanic winters.