Most 64-bit systems have a 64-bit time_t, so this won't affect them. Some 32-bit systems have also shifted to a 64-bit time_t. But it will be an issue that'll require a lot of recompiling and patching of ancient legacy stuff.
Even on 64 bit platforms with 64 bit time_t you are assuming that time is always stored in time_t, and never stored in or exchanged with systems that still use 32 bit time values. That's by no means a safe assumption.
OpenBSD is in the process of doing an upgrade to 64-bit time_t. Well, of figuring out the best way to do it. They seem to have most of it worked out, it's just a question of when to pull the trigger.
