It's not out of the realm of possibility. He's been the Yanks' best long reliever of the spring (so far). Including today's scoreless set of innings, he has not given up a run (albeit in just nine innings), recording nine strikeouts with just two walks and five hits. He's an effective pitcher at the Triple-A level, and that usually translates to (some) effectiveness at the major league level - perhaps this is the start of that.
The other main contenders are Phil Coke, Brett Tomko, Dan Giese and Al Aceves. Coke might draw attention because he's versatile: he can throw 96 MPH for one inning, but has the repertoire to go 3-4 innings if needed.
Tomko has pitched well, garnering a 1.74 ERA in 10.1 innings in the spring. But his long track record indicates otherwise: a 4.68 ERA over 1700 major league innings (mostly in the NL), he hasn't had an ERA under 5.00 since 2006, and he's 35, so he should only get worse.
Giese gave quality innings last year as the long man (3.53 ERA over 43.1 innings), and has a solid minor league track record (2.89 ERA over 10 seasons) but has sucked in ST so far (6.10 ERA over 10.1 innings).
Meanwhile, Aceves has been even worse. He's allowed five runs in seven innings (for a 6.43 ERA) - ironically, he was the best of the bunch last year, throwing 30 innings at a phenomenal ERA of 2.40.
How much weight does Girardi put on spring stats? It will be a tough call for him, but if it's not Igawa, they might as well trade him. There are several guys ahead of him on the minor league depth chart, and a few more coming up right behind him.