[victorNicollet]

The atmosphere is estimated to have ~830PgC worth of CO₂, and plants are estimated to photosynthesize ~120PgC worth of CO₂ every year, so a given molecule would have 14% chance to be broken down in a year. The probability to survive for 2000 years would be around 1e-60.

Of course, CO₂ contents of the atmosphere have varied over the last 2000 years, and not all CO₂ is produced into or consumed from the atmosphere (it can be dissolved in surface water, etc).

EDIT: since there's much more O₂ than CO₂ in the atmosphere, a given O₂ molecule has a 8% chance to not be broken down by respiration over 2000 years.