No, 15.625 msec is the period of the clock tick interrupt. Which lets the scheduler interrupt a thread if it has been running without blocking and the scheduler decides that another thread should get a turn.
Threads that block will be pre-empted at their WaitXxx() call. Or Sleep() call. Regardless of the clock tick interrupt.
Notable as well is that a sleeping thread can only resume running at a clock interrupt tick, the reason that Thread.Sleep(1) in fact sleeps for 15.6 msec. Timers, DateTime.Now and Environment.TickCount also have that accuracy, the clock is incremented by the interrupt.