A site is not barred from showing up in other countries because of the domain. As with most things search engine, content, quality and web popularity are the key factors. As an example, we run a .co.uk that sits happily on page one in the USA, Australia etc.
Having said that, there is evidence that major search engines give a small degree of preference to neutral tlds .com .net etc. Also bear in mind that regardless of domain, a site will only show for meaningful searches in "Pages From...." when the site is hosted in that location. IP address, along with country specific domain are strong signals for search engines in general.
Your .uk.com will be treated as a UK domain, not a .com. From the point of view of neutrality, the .net may be better, although that is not meant to be conclusive advice. There are many options when trying to resolve international exposure needs. From geo-targeting sections of one site, to running separate sites.
Often the best solution is one strong site but depends on language needs, your overall business and marketing plan, available resources etc. etc.
If you want to post more detail, people might be able to help further but regarding your basic question, the .uk.com isn't likely to be the answer.