the round losses do not need to be consecutive. if you win winners round 1, lose in winners round 2, then win many rounds through losers bracket, then lose in losers finals, you'd be eliminated then and there in losers finals.
as another example, in a 64-man bracket where everyone starts in winners round 1, a bracket run of win-win-win-loss-loss is the same exact result (tied for 5th) as loss-win-win-win-win-win-loss.
to clarify, brackets are only concerned with the binary results of sets. sets are made up of individual games. brackets don't care if you won your set with a 2-1 or 2-0 individual game score at all (these are both just set wins); brackets are only concerned with the matter of whether or not the set was won or lost.
there are some contexts (basically never brackets) where the individual game scores matter. these would be things like round robin pools, where there may be ties that need to be broken to determine seeding. but in terms of brackets, only the win/loss binary part of the set result matters.
you could view it that way, yeah. it's the fair way to do it, though, since double elimination is basically about playing out bracket sets until everyone but 1 competitor has accrued 2 losses. it wouldn't be fair to the winners bracket finalist if they get eliminated after losing only 1 set when everyone else had to lose 2 sets to be eliminated.