Does the LEGO (online) store ensure customers do not get repeated models in character packs?
I think I can answer this question myself now.
I have ordered twice, ordering five character packs in each. Across each of the sets of five, all of the characters I received were unique. However, there were two models in common between the two sets of five.
As zovits and Phil B. suggested in comments, it looks like employees will simply grab the next packs you have ordered form the box. Inside the box the packs seem to be ordered, so it is very likely that you'll end up getting unique models, but not assured.
If you would like all ten models, and can afford it, order ten packs at once.