How does the runtime of the Ukkonen's algorithm depend on the alphabet size?
As @jogojapan mentions in the comments, hasing generally is only amortized $O(1)$, so you would only get amortized bounds for the algorithm. However, I think you do not even get these: In order to get amortized $O(1)$ hashing, the hash tables have to be of size $\Omega(\Sigma)$, so you still have $\Theta(m\Sigma)$ space (and the same time requirement for initialization).

What's more, in practice the time for setting up all these hash tables will be much higher than the time to set up arrays.

You might fare better with using a global hash table that is indexed with (node, character)-pairs, but at least the "only amortized" argument will remain.