Hi,
I don't know if you've read through the
Guide to applying for EOI . I guess the EOI stage is one where INZ scrutinise all your details to assess how many points they think you can get and how suitable you are for residency. Based on this assumption, I would think putting in any relevant information that could help with this would be a good thing.
I haven't filled in an EOI myself so unfortunately can't give much help but, no doubt, others will be along soon to answer your queries.