Well, I'm not sure what VCE does, because they do their ligands completely wrong! The formula should be:
[Cu(NH3)4(H2O)2]SO4
The SO4 2- ion is just a "counterion" to balance the charge of the overall complex in the square brackets. Copper is in an octahedral 6 coordinate complex, with the ligands NH3 and H2O.
NH3 and H2O are the only ones you show the dotted lines linking to, because they are the actual ligands. The SO4 2- "counterion" only balances out the +2 charge that the copper centre possesses, but it is only an electrostatic attraction (as opposed to a ligand interaction, i.e.: the dotted lines you use in VCE).
We don't have to draw in the counterion when it asks to draw the complex, right?
Nope. If you want to be safe, you can just draw the complex, put it in square brackets, with the charge outside, then draw the SO4 2- ion next to it (and there wouldn't be any dashed lines indicating an interaction... it's just how you write ionic structures, you write the cation then the anion).