Short answer...yes.
Long answer, it depends on how it affects them and how it affects their relationship. I have bad anxiety too and if us being together and not being able to work things out would be bad for either one of us (or both), I wouldn't want to be romantically involved with that person.
You, for example, say you love yourself and are an oversharer. I would be much, much more likely to date you than date somebody who on the first date told me they hated themselves and had trust issues. Granted, trust is something that takes time and I can accept, but if from the get go things are looking bad, it's not exactly drawing me into continuing things.