That's just a state monad, the thread and what I assumed and may have assumed incorrectly you were talking about, was around overloading math operations to work on dimensionalized quantities like feet and seconds and the like. You can dimensionalize time as well—take a look at the time or thyme Haskell packages for some fascinating examples.
Doing computation in the context of the current time is absolutely monadic. If you're handling time abstractly, it's the state monad. If you're handling it for real then you need some kind of monad protecting communication with NTP/your local CPU clock. That's IO in Haskell.
Yup, you assumed incorrectly. I can see the qualitative difference between operator overloading and monads. That's why I suggested to transfer the core idea of monads into more mainstream languages to provide more "semantic" safety, so to say.
