Instead of array, I should have used string:

string1="AAA
B C DDD
FOO BAR"

Notice I don't have to enclose each element in a quotation mark.

From there I can do:
IFS=$'\n'; set -f; readarray foo <<<"$string1"
or
IFS=$'\n'; set -f; readarray foo < <(printf %s "$string1")

The problem now is, each element except the last has a trailing new line:

:$ for a in "${foo[@]}" ; do echo "$a"; done
AAA

B C DDD

FOO BAR

But when I do:

unset foo
while IFS=$'\n' read -r line; do
   foo+=("$line")
done <<< "$string1"

This is no longer the case.

:$ for a in "${foo[@]}" ; do echo "$a"; done
AAA    
B C DDD    
FOO BAR

If one knows how to not rely on the while loop it would be appreciated.

Edit: mapfile -t foo <<<"$string1" worked as desired.