Expecting any wicketkeeper to be as good a batsman as Adam Gilchrist is obviously very silly, and hardly anyone with any cricketing sense would be expecting such a thing. A more reasonable question would be whether he'll be as good as a "good" rather than "excellent" Test wicketkeeper-batsman like Healy.
Don't be fooled by Healy's overall Test career average: he was very poor at the end of his career (like so many are) which distorts it a little. But more significantly, he was very poor for the first half of his career and damn good for the second half. Haddin is unlikely to have a Test career much longer than half of Healy's, so he is in a sense at an advantage - if he equals Healy's "good" period and that ends as his entire career, he'll obviously look better because people will judge Healy as if his bad and good were all one, which, well, they weren't. Healy averaged less than 22 in his first 47 games in his first 4 years as a Test player, then just under 36 in his next 59 in his next 5-and-a-half years. So he was very poor for a fair while then damn good for a fair while. If Haddin cannot manage something similar, then for mine he's not as good, even if his career average should be, say, 34 to Healy's 27.
Healy also averaged 37.42 in the 50 matches he managed to fit-in for Queensland between 1987/88 and 1997/98. Not as good as Haddin's record for NSW (he averaged 32.96 in 45 games between 1999/2000 and 2003/04, then a really pretty awesome 54.91 between 2004/05 and 2007/08) but Haddin has played in an era where Australian pitches in general have been much flatter than Healy's.
So do you think Haddin has it in him to be better than Healy as a batsman? I'll be damn disappointed if he doesn't emulate him or come close, but I don't think he can really expect to do that much better. If he manages to play 60-odd Tests he'll have done pretty well, debuting at 30.