Short answer: No, 55% winning chance for the Inspector.
Here is a quote from the designer Bruno Cathala on balance in the game.
It is taken from a reply on Boardgamegeek
concerning balance of the game, i just want to give you some statistics.
The final balance has been made with testors belonging to the top of the mr jack players on internet (http://mrjack.hurricangames.com)
And, moreover, an artificial intelligence has been developped to help us.
I will speak here only about games played exactly with the final set rules.
If i consider games played by human player against an other human player:
196 games have been played
108(55%) won by inspector (96 by primal goal, and 12 after hunting jack because he got 6 hourglasses at the same time he was identified)
88 (45%) won by jack (53 by primal goal, 33 staying invisible after being hunted, and 2 by "dawn")
now let's see what happens when the computer plays against himself:
340 games have been played
187(55%) won by inspector (140 by primal goal, and 47 after hunting jack because he got 6 hourglasses at the same time he was identified)
153 (45%) won by jack (97 by primal goal, 55 staying invisible after being hunted, and 1 by "dawn")
So.. that's the reason why i know that the balance is slightly in favor of inspector, but not enough to really create a problem. (Experience and/or tactic competence is much more important to win ;-))
Hoping these results will interest you..
all the best