You won't miss anything whatsoever, if you're willing to play long enough.
The time limited events you mention are a set of quests that periodically rotate in and out of availability, according to this schedule. New event quests are still being added to the PC version, while older event quests are made playable after their original release.
In addition, every event quest is made available during time-limited festivals, lasting 3 or 4 weeks during certain parts of the year. The next such festival is the Spring Blossom Fest, which is most likely coming on April 26the Spring Blossom Fest, which is coming on April 26.