Absolutely. The coils are either copper tubes with aluminum fins or aluminum tubes and fins. They don't rust.
OTOH, they sit in a pan, often steel, that will rust, especially if the drain plugs up. All you need is a good cleaning.
The water comes from condensation of the evaporator coil. Clean the pan, clean the drain, then clean the coils with a spray made for that. You can do this yourself and should do it every year or so. At least check the drain.
Call the local VOC/Tech school and they may have a willing student to do the job.