No, our methods simply can't detect narrow spikes in past data:
"no temperature variability is preserved in our reconstruction at cycles shorter than 300 years"
This means if there was temperature variation in past data current methods couldn't detect it, so the absence of spikes in the data is not proof of absence. In other words, if global warming was reversed and 200 years from now temperatures went back to pre-industrial levels it would be undetectable 10000 years into the future with our current methods.