Hi skinnieh,
"Does that mean the Pulse Desktop Client will always try the first line (primary) first and then move on to the 2nd (DR)?" --- Yes, That's Right.
"For your second question" --- If the first URL responds fine then pulse won't fallback to the second URL & NO, pulse won't take it as a failure if the backend auth server is offline.
Regards,
Ray.

Pulse Connect Secure Certified Expert