They are immune to physical damage and cast nasty damage spells so its quite possible it won, yes.

Realistically you would have to keep trying new attacks and keep guessing at how to hurt this thing before it killed you (trial and error). In this game you only have to read the caption. Life would be so much simpler if everyone just had a caption and I could access their instructions.

I did the same mistake with auto-battling Banshees once - I learned very quickly from that

I both like and dislike things like this, mostly I like it.
- The good thing is that it forces you to use your head a bit - both when choosing to auto-battle, and when choosing how to gear your units.
- The bad thing is that even when you are overpowered you "must" still do things manually, just to make sure you don't get extra casualties.
On the other hand, such a risk is the price you pay for having things done for you.

the good news is - the banshee is really an exception. there are no other creatures in the world that are totally immune to physical damage. you'll make that mistake once, and remember it the next time just bring a champ with a damage spell or some weapon with bonus elemental damage -  or build a few guys with fire or frost staves or other enchanted weapons. if you bring mage to counterspell her wail, she's harmless.

there are other critters that are immune to certain types of damage (magic in general, or fire/frost/lightning/poison), but that's easy to overcome since most of your trained troops will deal non-magical, non-elemental damage anyway.

Banshees are easy.  One good flame dart and down they go.

I hate them with a white hot hate, but I am actually quite impressed by how dangerous those little banshees work out to be.  You really have to think twice about those things!!