This is a very good idea!
A few years back I had a slumber Birthday party for my DD, she was 13 at the time, at this stage, I didn't know all of her friends so she gave me a list of all her friends to be invited. About 17 in total. I always remember it because they did so much screaming - it was a nightmare.
At one point they all decided to run out in the front garden in their PJs. I called them back in.
This party was over 3 years ago. Recently we were discussing parties and I reminded my DD of that night they were so loud. She then said, " Yes, I remember it, when we went outside we saw Amy and her mum walk by - out on an evenings walk, I felt sorry for her" I was like what, why wasn't she invited, My DD just said she forgot to add her on the list.
Even after 3 years, hearing this - I felt physically sick, thinking of the poor girl walking past out hour house with her mother - not invited.
Errors do happen! You should message the mum privately - say no issue if they're not invited, per the above post.