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In polyphonic writing, you aren't supposed to use parallel octaves or fifths, but does that apply to, say, this situation(inner voices are not yet filled in for the second shown bar):
Where there are technically parallel octaves between the basses and sopranos, but they aren't rhythmically aligned. Does the rule against parallel octaves and fifths apply when they are not rhythmically aligned, like in the example above?
Yes those are still considered forbidden parallels. Fux, whose book is the basis for most modern textbooks on the subject, explicitly addresses this situation. The fact that the onsets of the notes occur at different times does not affect the fact that they move in parallel from G to F.
This reasoning behind why a soprano move from B down directly to F and a G-F move in the bass is also forbidden in Fux. The idea is that, based on the performance practice of the day, the soprano would fill in the "missing" A and G between the B and F, thus creating a parallel octave.
