No, it does not affect the registration of your trademark in any way. You'll need a legal representative who can apply for a trademark in the given country, but your domicile address does not play any role in the registration process or the application assessment.
However, please note that if you are applying as a physical person, your domicile address will be publicly accessible in the records as it is stated on your trademark application. If you disagree with your address being public, you can use a PO Box, except for the United States, where a PO Box is no longer accepted as a primary address.
If you apply under a company or as a legal entity, you must state your official company address. This address will also be publicly accessible via a trademark registry.