Does the math of CICO always work?

CICO always works, the energy always goes somewhere.

Both CI and CO is an estimate, so you won't know until after the fact which number you estimated was right or wrong until you test it out and see how your body changes. That is why it is important to properly track CI and as accurately as possible (stick to a certain method and dont change it) measure CO, and over time, make adjustments as needed based on results.

Roughly. As others have said, CI and CO are estimates.

One thing I think no one's said yet (unless I skimmed past it) is that the overs and unders tend to offset each other a bit (akin to the law of large numbers in statistics).

Two big areas where major discrepancies can arise:

• The TDEE or NEAT calorie requirement 'calculators' (they're really estimators). They give you an estimate of your needs from studies of large groups: They peg you at the average from those studies. But, in practice, individuals can differ from average by up to several hundred calories per day. They're the best source of a starting point estimate, but you should use several weeks of your own loss data to estimate your own personal calorie requirements, before expecting your weight loss to be somewhat predictable.
• Exercise estimates are pretty hard to pin down accurately. Many sources overestimate. There are better and worse practices to improve accuracy a bit, but that's a whole 'nother complicated discussion.