The `"` marks will not work here and won't save you :). Eg. this code:
```
a="b c d"
if (( "$a" > 2 )); then
```
generates an error `bash: ((: b c d: syntax error in expression (error token is "c d")`. If you use `if (( $a > 2 )); then` or `if (( a > 2)); then` the same error will occur.

Putting `"` here can cheat someone, that you can pass some multi-word arguments to this function ;).