As these two ladies have so clearly explained, "it depends". (By the way, that is a phrase used very heavily in the orchid-growing world.)
There are a lot of water-quality factors to take into account, and there are filter factors, as well.
Mechanical filters remove suspended sediment, but that's all, so do not really affect water chemistry.
Some (not all) orchids are particularly sensitive to the mineral content of the water. No filter will affect that. To reduce that, you will have to go to distillation, reverse osmosis, collected rainwater, etc. Some beginners buy spring water for their orchids, but more often than not, spring water is quite high in dissolved minerals, so it's no advantage to use it.
Chlorine is not an issue, as if you leave the water standing in an open container, the chlorine will dissipate overnight. If your municipality uses chloramine however, you're definitely going to need a filter (charcoal?) to remove it.
Organic compounds in the water are likely more of an issue for you than the plants, so if it's OK for you to drink, it's OK - in that respect - for the plants.
pH of the water and your fertilizer solution can also affect plant nutritional uptake and growth.
But before you can decide whether you
need to treat your water, or just
how to treat it, you need to know its chemistry.
If you have municipal tap water, your provider can give you a report, but you might also rely on a water quality lab to test a sample. I am on a well, and lab testing told me that the quality varied a bit over the course of the year, so I went with reverse osmosis, and have never looked back.
As to humidity trays, please read this:
Evaporation