Hashing would make this technique less useful, but not necessarily useless. For instance, if there is no salt involved, and the hashing algorithm is known (or guessable), you can still make some use of the information leaked.

The difference is that you are not being leaked information about the password, but about the hash of the password. One problem with trying to brute force an authentication over the internet is that it is slow and potentially noticeable by the server admin (then you get cut off). If you exploited a timing attack from a comparison between raw md5's or sha1's of a password, then you can use the leaked information to focus your brute force. Basically, you could use a rainbow table to help you pick what passwords to try next, getting a lot more bang for your buck. In this way you can use the combination of offline brute forcing to generate possible hashes, and the timing attack to select which passwords to actually send.

Now an unknown salt would still ruin your day, just like it is designed to make life difficult for rainbow tables in the first place.