Aside from the fact that the server is 64 bit, nothing prevents you from using a 64 bit time_t in a 32 bit app. Sure it won’t be native, which will slow it down a bit because it’d require more instructions for every action with it, but it will work.
Finally, to make my reply a bit more interesting, here’s my PSP with 32 bit Sony CXD2962GG CPU, on its way to embrace the two-o-nineties without visible confusion.
