I would answer the question clearly with 'NO', because the air evaporates via the filter, otherwise the part is useless and you can also put a kettle there. I use filters for one season at a time, then they go in the rubbish. Fortunately, it's paper.

My appliance was delivered WITHOUT a filter:(
I have now used it for 1 year without success and have been very annoyed about it. I didn't realise that it needed a filter.

You can. But I think little or no water evaporates. The filter is there to suck up the water and the fan blows the air through the filter, which then absorbs as much water as possible.