It's typical to use compressed air, clean rags, and a vacuum to pick up whatever is loosened during cleaning, so that should pose no risk.
You should verify whether they'll be using any cleaning solution during the process though.
The AC coils are inside the air handler of your HVAC system, so air will be blown over the coils even when you're just using the system for heating. If you can smell a cleaning product while they're working, I'd open the windows and take Widget outside, If you turn on the fan/heat and can smell a cleaning product (if used), I'd keep Widget outside while the fan runs with some ventilation windows open until you can no longer smell anything.
Here's a visual of what's going on...
I trust it needs to be cleaned if they're saying it does, but I'm curious to see if the cleaning has a positive effect on your humidity issue, because it doesn't strike me as particularly relevant unless AC is being used.