Barrier #2 guarentees that the write to _complete gets committed immediately. Otherwise it could remain in a queued state meaning that the read of _complete in B would not see the change caused by A even though B effectively used a volatile read.
Of course, this example does not quite do justice to the problem because A does nothing more after writing to _complete which means that the write will be comitted immediately anyway since the thread terminates early.
The answer to your question of whether the if could still evaluate to false is yes for exactly the reasons you stated. But, notice what the author says regarding this point.
Barriers 1 and 4 prevent this example
from writing “0”. Barriers 2 and 3
provide a freshness guarantee: they
ensure that if B ran after A, reading
_complete would evaluate to true.
The emphasis on “if B ran after A” is mine. It certainly could be the case that the two threads interleave. But, the author was ignoring this scenario presumably to make his point regarding how Thread.MemoryBarrier works simpler.
By the way, I had a hard time contriving an example on my machine where barriers #1 and #2 would have altered the behavior of the program. This is because the memory model regarding writes was strong in my environment. Perhaps, if I had a multiprocessor machine, was using Mono, or had some other different setup I could have demonstrated it. Of course, it was easy to demonstrate that removing barriers #3 and #4 had an impact.