Is the output of an aggregator component in Informatica always going to be sorted by the group specified, also when the input sorted box is not ticked, and the component does the grouping itself? Or is there no guarantee?
If your input to the aggregator transformation is not sorted, then the output will also not be sorted.
As for your other question, even if you do not use sorted input , aggregator transformation will group by just fine. It might only impact performance.