Maybe, but currently most 32-bit Linux time code breaks on negative value
time_t was never intended for date manipulation (though it ended up that way). Some 32-bit time_t libraries I have tested do work for negative time_t, others are broken (probably as a sanity-check as that is not a supported operation). In most cases what matters for code is getting the current time correctly, and interpreting file time stamps, etc.
If you need to work pre 1970 and post 2038 there is no simple 32-bit integer solution possible and then you have to make 64-bit changes, recompile, test, etc..