Yes(ish). But you will need to help them.
There are several ways that Google, for example, will relate domain names.
1] Registration information. Make sure that the owner contact of the original and new domain match and that the contact information match. If this is not possible, then do the best you can. If these match, Google will credit the new domain with some small amount of trust and begin to make some assumptions.
2] On-site contact information. It is highly advisable that the About and/or Contact page of each domain contain contact information about the other site (if they differ or the same if they do not) as well as a link. In addition, schema.org mark-up should be used. Mark-up is trusted by Google more simply because there is no confusion what the data means. Using the contact information and links will relate the sites. This should include as much as makes sense including address, phone, e-mail addresses, etc. E-mail addresses are a particularly valuable data element.
3] Any personnel profiles. While most businesses forget this, personnel profiles are a strong additional signal to relate web sites. Again, use mark-up and as much information as you can including e-mail addresses. There should be some overlap between the sites or this will not work. Overlap can be CEO contact information for example. It can also be technical support, sales, etc.
4] Links from the home page. A simple link from the home page does not hurt either. Just do not make site wide links in headers, footers, or the sidebar. While there is some tolerance for this, I do not suggest risking a penalty.
5] Simple citations. A citation is a mention. In your content on both sites, mention the two sites in relation to how it fits best. You do not need a link per se', just a mention. A link could be good along side a citation. Since citations are a signal as well as link, why not use both?
6] Home page title. And any other page title that makes sense, place the company name. If you manage the title tag properly, you should be able to brand each site: one, the local/regional site; and two, the international site. Do this how you see fit. Branding title tags is a strong signal. Make them similar, but not identical.
That should be enough. You do not need all of these things, but strive for as much as possible and give as much detail as you can that makes sense for your situation.