Can the work history be verified? Sure. Companies often outsource that sort of thing to background check firms which generally don't have a problem calling up companies in foreign countries to validate employment. Obviously, background checks involving foreign companies may be a bit more involved than those involving local companies but it's not terribly uncommon so it normally works reasonably well. Obviously, though, it's easier in some countries than others-- it's easier to validate employment that happened in England than it is to validate employment that was in Syria. Since your work history was with a large multinational company, though, it should be relatively easy to verify.
Some companies do verify background others don't. Most larger companies do at least some sort of background check. Whether that involves just a criminal background check, whether that involves calling your references, or whether that involves contacting each of your former employers is very company dependent. If all your experience is in a foreign country, it may be more likely that the company decides to do a more thorough check than if your experience is local but that's going to be very dependent on the company and possibly the hiring manager.