From what I've seen, users generally expect links on 'header sections', and are likely to try and click to see what they do if it is something in which they are interested.
Breadcrumbs give a sense of hierarchy and since they change as a user navigates, they give the user a sense of where they have been. Implying that they could get back to a higher level some how, possibly by clicking.
Underlines and color changes are nice visual queues to help the user, and do make it more obvious that there is some interaction that can be done, but given that there are so many different styles of apps and websites out there, it seems it is becoming less common to have underlines on navigation.
If you are hard set on the design, I suggest leaving the bread crumb navigation as you have it. The very fact that it is where navigation is expected, on the 'header section', and that it looks like a breadcrumb should be enough to promote clicking.
Another thought, if you are targeting mouse, then a subtle hover state on each breadcrumb link would give some additional assurance to the user that they can click on the link and go somewhere.