Short answer: no — a published collection corresponds to exactly one label. When you publish "Label 1" as a collection, only that label travels with the verses. Any additional labels you have on those verses (Label 2, Label 3, Label 4) stay on your own account and aren't part of the upload, so subscribers won't see them.
If you want subscribers to receive multiple groupings for the same verses, the workaround today is to publish each label as its own collection. A user who subscribes to several of them will end up with the same verse referenced under each label (the app deduplicates the verse itself, but the label memberships come through).
I'll note this as a feature request — letting a published collection carry a verse's full set of labels (or letting a publisher bundle several labels into one collection) would be a nice extension. Thanks for the clear example!