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It appears that there is a small effect on the amplitude of the annual change in CO2. The 2008 amplitude (difference between high and low of the annual CO2 levels) centered around 2008. You can see the effect if you put a ruler connecting the highest annual CO2 peaks and repeat that for the lowest CO2 minimums.

The deep water ocean currents take hundreds of years to transfer CO2 from the downwelling surfaces near the poles to the upwelling surfaces near the equator. We could be now seeing the effect of enhanced CO2 absorption during the little ice age. The amount of desorption occurring at the upwelling surfaces depends on how much CO2 is upwelling as well as the temperature.

In other words, waters that contain greater amounts of dissolved CO2 than average are now surfacing. The surface temperatures at the downwelling areas are warmer now than what they were when the present upwelling currents received their load of CO2 hundreds of years ago.

The temperatures at the downwelling and upwelling areas are probably what control the mechanism I mentioned. Since the temperature in the plot shown in your link is for global sea temperatures, I don’t know for sure what the upwelling and downwelling temperatures are.

Yes, a very good point, the ocean buries the CO2 or releases it depending on the polar temperatures and particular the melt and refreeze. It is the refreezing itself that causes the downwelling since the remaining water becomes more saline and heavier and sinks to the bottom. But one mitigating factor is that the ocean turnover rate is very slow and so the sequestration of CO2 is very slow (or that's what the catastrophists would like us to believe). Second, the global SST which I linked to is much more important to the immediate absorption of CO2. But again, not so important that it has any kind of overwhelming effect.

The 2008 dip is very real but pales in comparison to the annual rise and fall of CO2. That implies that vegetation is much more important than SST over the short run. That suggests fossil fuels are too (over the short run). Your sequester/release mechanism is viable over the long run but would require extremely rich-in-CO2 upwelling areas to be a factor in the short run. I do not recall reading anything about such areas in the present oceans, but I have not read a lot in that area.