In the 800 kyr $\ce{CO_2}$ record, how detectable would a short-term peak be? It is stated in https://cdiac.ess-dive.lbl.gov/trends/co2/ice_core_co2.html that the temporal uncertainty for the glacier $\small\mathsf{CO_2}$ records is less than $\small\mathsf{5~\%}$ at any given moment. That means ‒ for example ‒ ca. $\small\mathsf{5,\!000}$ years at $\small\mathsf{100,\!000}$ years ago.  Could there have been peaks in the $\small\mathsf{CO_2}$ record that rose and fell back so quickly we wouldn't be able to detect them? Is there some paper or perhaps a monography that lists all the possible events in Earth's history that could have occurred in the last $\small\mathsf{800,\!000}$ or more years, which would lead to a likewise fast $\small\mathsf{CO_2}$ increase as today's, but also showing that, on the other hand, any such events would leave a long-lasting trace in the $\small\mathsf{CO_2}$ that should be easily detectable in the record?

I've found out that part of the answer is already in answers to this question.
$\small\mathsf{CO_2}$ does not fall back quickly:


  graph shows the IPCC 2007 $\small\mathsf{CO_2}$ liftime from a computer model run that shows what happens to a single instantaneous pulse of $\small\mathsf{CO_2}$ emitted to the atmosphere. One thousand years after the $\small\mathsf{CO_2}$ is emitted to the atmosphere 20% is still there according to this model.
  only zero carbon
  


The decline shown is mostly due to $\small\mathsf{CO_2}$ dissolving in the oceans.