Apparently she requested an extension from her job, and the intention was to extend her gap year for a year. So we really don't know what the reason is.
I believe Chelsy and Kate became friendly as they were dating the brothers. If that friendship became something that extended beyond just being girlfriend (like they became true friends), we might see that if she comes to the wedding. I guess we will never know if she was invited because she is Chelsy who is a friend of the bridal couple or Chelsy who used to date Harry and is now his date.
I only reference that is because once I was invited to a wedding as myself, and my boyfriend (soon to be ex) just assumed that I was his plus one. I had to tell him that I was invited basd on my personal merits. If that makes sense. But I don't think we will ever know for sure what is the case for Chesly.