Yes, mutlithreading could certainly do this, but be weary that threading is usually more complicated than the alternative (which would be the main thread polling various update events as part of its main loop, which should be running at least once every 100ms or so anyway).
In your case, if the clock thread follows pretty strict rules, you'll probably be "ok."
- The clock thread is the only thread allowed to set/modify the time variables.
- The main/ui thread is only allowed to read the time.
- You must still use a system time function, since the thread sleep functions cannot be trusted for accuracy (depending on system activity, the thread's update loop may not run until some milliseconds after you requested it run).
If you implement it like that, then you won't even need to familiarize yourself with mutexes in order to get the thread up and running safely, and your time will be accurate.
But! Here's some food for thought: what if you want to bind in-game triggers at specific times of the day? For example, a message that would be posted to the user "The sun has set" or similar. The code needed to do that will need to be running on the main thread anyway (unless you want to implement cross-thread message communication queues!), and will probably look an awful lot like basic periodic-check-and-update-clock code. So at that point you would be better off just keeping a simple unified thread model anyway.