No, when a user requests a domain the first Domain Name Server queried will be local to them. Only if no record is found will the request be passed 'up the line' to the next Domain Name Server. It is possible that the request will get all the way to the registrar's DNS but it is unlikely and in any case it happens very quickly (YMMV!). It's not really worth worrying about.
However the location of the webserver that a site is hosted on may make a difference to your search engine visibility in different countries depending on the domain name itself.
This is not normally an issue where your domain matches that of the country you are hosting in but will unless you take some precautions/actions.
An .fr domain hosted in France will not be a a problem.
An .fr domain hosted in the USA may not be indexed in the google.fr or will receive lower rankings than pages that are obviously related to French users.
You can overcome this by using, for example, Google's webmaster tools to indicate which geographic regions your site pertains to.
You should also be sure to make sure you declare the appropriate languages in you HTML.