As somebody who works in the field of chaos theory (for whatever that’s worth), I confirm Dmckee’s assessment: There is no reasonable relation to any concepts from chaos theory.
There is, however, an attempt in your quote to relate this to the phenomenon of criticality – which is not chaos theory, but like chaos theory is related to the field of complex systems.
Applied to e-mails, the concept of criticality can be summarised as follows:
Let $φ$ be the average number of e-mails sent as a consequence of a given e-mail.
If $φ<1$ and there is no mechanism (other than other e-mails) causing people to sent e-mails, e-mails will eventually die out.
If $φ>1$, there is an exponentially growing cascade of e-mails and we will eventually drown in them.
Therefore, there is a critical point at $φ=1$ separating the two phases described above and marking a phase transition.
However, I cannot see any reasonable connection of the above concept to your quote. The time a given person spends on e-mails does not affect $φ$ in general and thus there is no critical point to cross when increasing the time you spend on e-mails. Moreover, this is neither unpredictable nor invisible nor is there a cascade involving the rest of one’s workflow.
Finally, I fail to see any other way to apply the concept of criticality to e-mails.