Hi James
The short answer is 'yes and no'.
Solely Local SEO doesn't usually affect International SEO at face value, as local is local and international is everywhere, as I think you already know from your question description (though read on below...)
However, just about any aspect of SEO can affect the SEO of a webpage and a website from the overall bigger perspective. There are lots of common factors between local and international SEO, as well as some differences. For one website that is trying to cater for both, there will be compromises to be made in some instances, plus some advanced SEO to take care of too.
You'll find http://searchengineland.com/local-seo-international-seo-have-lots-in-common-47937 an interesting and helpful read on this topic.
An example, an IP Address can have a different effect on local SEO efforts than International efforts (i.e. location of where the website is hosted).
There are language differences, user behaviour differences...
I'd suggest reading that article and then figure out who you're targeting, where and how. The answer could end up in needing more than 1 website, subdomains for different geo-locations, a site/cms language translator...
Hope that helps,
Regards
Simon