This is a good question! Not sure which precise units they had and in what quantity, but given the size of the Titan (no way they can support liquid regenerative system with their size and energy reserve constraints), they would have had canister containing solid CO~2~ adsorbent with a fan (example).

Without the fan, it's not going to be very effective since CO2 has to actually pass over the solid. Passive diffusion is not going to move the same volume of CO2 over the solid even if the solid was removed from the housing. Even if they didn't run out of battery, The solid has a maximum capacity - about 7.5 kg for the unit linked above. Even with reserve capacity, an average human exhales ~0.97 kg of CO~2~ per day.

O~2~ to CO~2~ exchange via respiration is mole for mole (you do lose a little mass in carbon and water just by breathing!). Atmospheric CO~2~ is 0.041% (410 ppm) and O~2~ is a hair under 21% and that's the standard to which life support systems are held. Humans lose consciousness at around 3.7% oxygen, but experience hypercapnia at >6% CO~2~. (Physiology nerds - I converted from the partial pressures in mmHg to % of 1 atm for comprehension)

So in this hypothetical scenario, hypercapnia would definitely precede loss of consciousness due to anoxia.