I am wondering if any game designers have used an online implementation of a game to balance and tweak it before commercial release.
I'm pretty sure "Day and Night" was tested online before release. But the online game was only limited to a small beta testing audience. The website used to say that the online version would reappear at some point, but the website is now dead and the developers appear to have vanished.
Since Day and Night is an asymmetric game, getting the two sides balanced is important, and the developers claimed that they were very close to 50:50 based on online testing.
VASSAL offers a way to create on online version of a game easily. I was involved in play testing Crown of Roses using a VASSAL module. The map for Clash of Monarchs has been critised as being difficult to use and the reason provided for this was that most of the play testing was done online which had a much clearer map.
Donald X. Vaccarino, the designer of Dominion, tested it with a program he wrote himself. Later expansions were playtested in a private room of the Isotropic online Dominion server. He discusses it briefly here:
I did not know Doug prior to him making isotropic; Wei-Hwa knew him. Before isotropic, I used a DOS program I wrote in Pascal, cbtest. It didn't do the internet part, we handled that via irc.
(Doug is dougz, the creator of the now-unavailable Isotropic Dominion.)
I was a beta tester for a few of David Sirlin's card games. Most of the beta testing was done online, in a combination of LackeyCCG and a very rough alpha web client for Yomi. I actually put some footage up on YouTube.
Someone brought up the objection that writing an online client is much harder than just designing the game. While it's true to an extent, you can cut a lot of corners if you're just testing. You don't need a lot of flair, or rules enforcement, or even "something that isn't dog-ugly", and your early testers won't care because it's not a finished game anyway.