Dissolved CO2 will definitely cause the TAN to increase. You may want to be careful when removing the CO2 to prevent any other volatile acids (formic acid, HCl etc.) from being pulled off the sample as well.
No disrespect to Fuchs formulating ability, but POE and CO2 is a recipie for eventual system problems. The only way to protect the POE from decomposition by acid attack is to manage the temperatures in the system to prevent chemical reaction. CO2 tends to have higher discharge temperatures than traditional refrigerants so this is no easy task.
CO2 is such a small molecule, you will not be able to fully protect the ester linkage from attack by using steric hindrance from acid chain branching. Acid scavenger additives (epoxides etc.) that can be used to protect against autocatalytic attack with traditional refrigerants will be consumed by CO2 itself. POEs are just not a good choice in either acidic or caustic environments.
If you are curious and have the suitable glassware, you could run a hydroxyl number (by reaction with anyhdride) on the POE to look for alcohol groups formed from POE hydrolysis. Normally, the hydroxyl number is used to measure the degree of conversion of the POE during manufacture. Expect to see hydroxyl numbers less than 5 on high quality POEs. If the hydroxyl number is going up, the POE is coming apart.