No it did not break chain of custody, to put their ballot in a secure ballot box, to have their vote, counted later.
In fact, that is how voting is done everywhere in Arizona, with early voting. The citizen when voting early, puts their ballot in a ballot drop box, to be counted later.
And every vote counting machine, if not able to read your vote, has drop box #3 attached to it, so your vote can be dropped in to it....to be counted later.... It's not like the machines have never had problems reading the ballots before, they occasionally are unable to read them, so the #3 drop box has always been part of a back up plan.