If the question is did it have a chance: Sure. All shows that are nominated do. Was it anticipated to win? No, not really. To understand why, you'll have to put your personal opinion about the show (which I share) aside and look at it from a historical perspective.
Spamalot was the huge, and I mean HUGE, hit of the season. It had the highest grosses, it had generally the best reviews (including a rave from the NY Times), it had a company of actors that were well liked within the community led by theatrical legend Mike Nichols directing his first Broadway musical in decades and the most nominations of any musical that year.
While Piazza was certainly very well liked on here (with a few dissenters), its reviews were kind, but not enthusiastic (with Brantley essentially saying it had high hopes and reached them sometimes) and even at the subscriber based LCT, it was not selling well.
What's interesting is that Piazza ended up having a much better outcome on Tony night than people expected. And Spamalot did a lot worse.
Yes, Spamalot won Best Musical, but it only won 3 Tony Awards total, which is far fewer than many Tony pundits predicted. There was an expectation of a sweep similar to The Producers with Spamalot, with many thinking Piazza was only a lock for Victoria Clark and probably orchestrations. There were many who were shocked that Piazza did as well as it did with its nominations and found it a fluke and thought voters would find the show dull and cold and would gravitate much more to the brassy Spamalot or endearing Spelling Bee. Instead, Piazza ended up surprising a lot of people by sweeping the design categories (many thought Chitty Chitty Bang Bang would win set design) as well as score and ending the night with the most Tony wins and a stellar performance.
It didn't win Musical and no one thought it would. But its success that night exceeded almost everyone's expectations, allowing it to run for over a year, have a national tour and a live broadcast on PBS. All things no one expected.
"Sing the words, Patti!!!!" Stephen Sondheim to Patti LuPone.