Yes, it is perfectly possible. As I've discussed here, it is possible to convert generally contracted basis sets into (somewhat) segmented sets without any formal loss of accuracy; next, one would discard functions with tiny coefficients and reoptimize the segmented exponents and contraction coefficients to end up with a segmented basis set.
However, as you (or your lecturer) said, segmented basis sets are much less beneficial for correlated calculations than SCF theory, since whereas SCF is usually dominated by the cost of forming the Fock matrix (i.e. calculating the two-electron integrals), in correlated calculations the cost of forming the integrals is often small compared to the post-HF calculation itself. For instance, the traditional AO $\to$ MO integral transform has a $\mathcal{O}(N^5)$ computational cost, while CCSD has an iterative $\mathcal{O}(N^6)$ computational cost.
Also note that the Karlsruhe def2 sets employ segmented contractions, and the sets with two sets of polarization functions (def2-TZVPP and def2-QZVPP) are aimed for post-HF calculations, so you should be able to find out the speed difference yourself by comparing calculations in the def2 sets to corresponding ones with the cc sets.
Addendum: I should also mention the Sapporo basis sets, which are likewise segmented and optimized for post-Hartree-Fock calculations.
