If OFDM did not have a cyclic prefix or zero padding would have equalization of the individual sub-carriers been possible in the frequency domain?
To extend on P2000's answer:
So yes it's possible.
and he even tells you what kind of equalizer might be worth looking into.
However, in almost all cases (there's a few sparse signal speciality channels out there), you do OFDM to avoid having such a complicated equalizer.
So, when using a long (and thus, complex) equalizer, why still use OFDM? If you've done your equalizer right, your channel is flat afterwards. If you do (classical) OFDM right, you don't need the equalizer.
There's a few corner cases (and those are very real) that could benefit from a combination, but seriously, reading your questions, you're not designing one of these. You're trying to understand what OFDM is about. And OFDM is mostly about not needing an equalizer.