Of course it will. Compared to normal walking, does your energy level drain faster if you run?
Mechanical chronographs are all different, but I find that a running chrono eats up a power reserve about 15% faster (i.e. 48 hour PR gone in about 36 hours) than when the watch is just in time telling mode.
In a mechanical watch, it is more a question of wear and tear. Engaging the chrono will affect the amplitude, and a lot of chrono modules are not jewelled. The barrel does not unwind any faster, the escapement determines the run time. The power reserve remains the same, and since we are talking about an auto chrono, as long as you are wearing the watch and moving around, the power keeps replenishing. In a quartz chrono, however, running the chrono constantly will affect your battery life big time. The reason quartzes use so little power is that they only tick once per second. That means the watch is at rest in between, with no power drain. That said, I suppose the last rotations on the mainspring, being weakest, (assuming you just placed the watch on your dresser and let it run itself down) might not be enough to run certain watches in chrono mode quite as long as regular mode, but the difference would be minimal. Some chronos, like some IWC movts, are designed to have virtually no difference in amplitude with the chrono engaged, with extremely low friction, and would have virtually identical runtimes.
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