Google Search will still show your site in all other countries.
My experience says that selecting a country will allow Search Engine to give preference to your site in that particular region. But still it all depends on the overall ranking/authority of your site in the search results of Google Search Engine which depends of many other factors.
As far as i have experienced, it has no major effect on search ranking of your site in that region, rather it is of minor importance at the moment. It might get serious in coming days, who knows :heiligenschein:
It is recommended that targeted region should only be selected if you are 100% percent sure that the targeted users are in that particular country only, otherwise leave it as international and let the Search Engine decide the targeted regions for your site :whistling: