When drawing resonance structures, it is permissible to alter the way atoms are connected?
It depends on what you mean.
If you are saying specifically switching the positions of atoms, then no. You would have a completely different molecule.
If you are talking about conjugated pi systems, then yes, if there is resonance stabilization all throughout the region you are considering, you can "shift" the electrons or double bond(s) throughout that region (in reality, the electrons are just mobile throughout that region).
For example, acene sheets (such as (5a, 4z)-periacene, which has 54