In theory, an optimal strategy, in the sense of a Nash equilibrium, certainly must exist. However, based on the description of the game on Wikipedia, I see some difficulties in finding such a strategy in practice.
First, it appears the the game is non-deterministic, so the optimal strategy can only be optimal in a statistical sense — it cannot guarantee victory for any player. Second, the outcomes of different moves appear to depend on the physical properties of the blocks, which means that calculating the optimal strategy would first require developing an accurate model of the game physics, and then fitting the model to actual measurements.
(That's not completely impossible — for example, it has been done for Pass the Pigs, but that's a simpler example, since the pigs in Pass the Pigs don't really interact with each other much. In that respect, Don't Break the Ice seems closer to, say, Jenga.)
Finally, I'm not sure how consistent the physical properties of the game pieces are, or how likely they are to change over time due to age or wear. If the behavior of the pieces varies too much, a strategy calculated for one particular game set may not be optimal for another one.
All that said, however, it might still be possible to come up with a deterministic (or at least consistently non-deterministic) approximation of the game, and then analyse that approximation. I'm not familiar enough with the game in question to suggest what such an approximation might look like, though, except for some very crude features (e.g. that completely disconnecting the center from the edges of the playing field should surely be a losing move).