Your coworker might genuinely feel like it helps, and that's worth taking seriously even if the science doesn't fully back it up. The thing is, people are terrible at assessing whether something actually works when hangovers vary so much depending on what they drank, how much water they had, how much sleep, etc. You could take charcoal one time and feel fine, skip it the next time and feel worse, and convince yourself the charcoal made the difference.
The bigger issue nobody's mentioned yet is that activated charcoal can actually mess with how your body absorbs other stuff - medications, vitamins, nutrients. If you're taking it regularly or combining it with other supplements or meds, it might be binding to things you actually need. That's worth knowing before you make it a habit just because your coworker swears by it.
So yeah, the timing arguments hold up (it needs to be *during* drinking if anything), but honestly the most reliable approach is just drinking water while you're out and getting decent sleep. I know that sounds boring, but it actually works way better than any supplement I've tried. Save your money.