I think (and this is solely my opinion. I have no government guidance or document that I can pray in aid), that being non-domiciled can be a problem when it comes to applying for British citizenship.
British citizenship has a future intentions requirement, that you intend to reside and settle in the UK. The concept of Domicile is very similar, where do you intend to settle in the long-term.
A non-domiciled person is in effect stating that they do not intend to reside in the UK, something that is at complete odds with the future residence requirements.
This withdrawn
document on the Gov.UK website gives an idea of the concept of domicile and how it is assessed.
More information on the future intentions requirement is in the
Naturalisation as a British citizen caseworker guidance, from Page 29.
I'd suggest that the OP consult both a lawyer specialising in naturalisation law and domicile AND a good accountant with an understanding of non-dom and domicile status.
I am not a lawyer or immigration advisor. My statements/comments do not constitute legal advice. E&OE. Please do not PM me for advice.