Which version of "Systems Engineering" are you referring to? There are no less than seven definitions of what it is as a disipline (this from the folks at the International Council on Systems Engineering -
www.incose.org).
Usually it refers to a person -- the "systems engineer", rather than a job description. There is typically only one person with the title of "systems engineer" even on very large projects. In the majority of definitions, it is a very senior-level position (akin to the Program Manager). That person is essentially the lead engineer of a project, and is responsible for ensuring that all of the various disiplines and stakeholders are communicating. As such, it requires experience with a broad range of engineering issues. SE has been around since the 1950's, originating with very large US Air Force development projects.
Although it might ultimately be a great career path, SE cannot be considered the starting point on that path because of the level of experience required (just like a Program Manager position). If a company were to start out a recent grad in a position like that, I'd be very, very cautious about such a situation.
Some of the other definitions of what SE is can be quite different, and much narrower in scope (especially in the fluid power industry). I'm referring to SE as described by ISO 26702:2007.