Won't any new update or iteration of SKSE break existing mods depending on the previous version though? I suspect there's going to be a lot of frequent updates during the alpha and beta phases, so I'll wait until things stabilize.
No, it depends on what is being updated, so not any new update or iteration. You must be remembering of updates on the game itself. Those break SKSE every time until the SKSE is updated with the new addresses.
That being said, it's is still alpha, so not recommended for everyone by default.