"${stuff[@]}" expands into the elements of the array, with each one quoted - so even that first "foo foo" element with a space will be handled correctly. That is how I would write the loop as well, in general.
However, your technique also works, with some tweaks:
* The loop goes one index too far, and can be fixed with seq 0 $(( array_length - 1 ))
* There should be quotes around ${stuff[i]} in case it has spaces
The bash syntax for arrays is obtuse and no one will spot when an error creeps in. It's worth to make an effort to say with space separated strings, as long as you are with bash. More advanced data structures is often an indication that it's worth glacing at something like python.
Should you need to handle spaces, it is often much easier to go with newline separated strings and use "| while read".
This contruction has the added benefit of the data not needing to fit in your environment. This can be a real issue, and is not at all obvious when it happens.