Is there a Time Hierarchy theorem for PH?
Yes. For example, the usual proofs of the time hierarchy theorem (by directly simulating arbitrary machines) can be used to show that for every $c \geq 1$, $\Sigma_c TIME[n^k]$ is not a subset of $\Pi_c TIME[n^{k-1}]$. The reason for switching from $\Sigma$ to $\Pi$ is that, in this diagonalization argument, we have to do the "opposite" of the machine we're simulating, so we have to run in universal mode when the simulating machine is in existential mode, and vice-versa.

You can also get a result like this without switching from $\Sigma$ to $\Pi$: for every $c \geq 1$, $\Sigma_c TIME[n^k]$ is not a subset of $\Sigma_c TIME[n^{k-1}]$. This can be done using the proof of the time hierarchy due to Zak (reference: "A Turing machine time hierarchy", Theoretical Computer Science 26(3):327--333, 1983). For an explicit reference to this version of the time hierarchy theorem, see Dieter van Melkebeek's "A Survey of Lower Bounds for Satisfiability and Related Problems" (available on his home page).