Can I secure a new non load-bearing interior wall to the existing ceiling and strapping?
Even though the wall doesn't need to bear weight, it needs lateral support so it doesn't tip over.  How much lateral support you need to satisfy engineering requirements and code compliance depends on many things, seismic requirements, type of wall construction, dimensions of wall, endwall attachment, etc.  If the wall will carry shelving or cabinetry, it needs more lateral support.  

Attaching the top of the wall to a structural member above is usually the easiest way to provide lateral support but not the only way.  It's possible to build partition walls that don't extend all the way to the ceiling above, usually by extending the end studs through the floor to attach to the joist below.  

Attaching to the strapping would provide some support but since strapping is part of the finish, non-structural, you can't really count on it for support.  It's also possible that the load on the strapping might cause some cracks or other blemishes on the drywall ceiling.  

In commercial construction it's common to see partition walls attached to the acoustical ceiling grid at the top, which would seem like a similar method, but it's debatable if attaching to the ceiling grid complies with current building codes.  

Bottom line, you might get away with attaching to the strapping, but installing blocking is the right way to go.