Yes. A board opened with Open a board shows the boards you came through as a breadcrumb at the top. The trail is kept in the address (?trail=...), so the Go back action and the browser’s back button both walk back along it.
One thing that catches people: a bookmark saved without the trail starts a new trail. If your operators bookmarked the third board’s address without its trail, they land there with nothing to go back to. Bookmark the first one.