A watch is designed to be shock resistant to a point, but there is no such thing as a shockproof watch. It is useful to note that shock resistance requirements are usually defined by the parameters A) does it still run and B) the acceptable range for loss of accuracy. These tests are also conducted under very specific conditions.
That having been said, mechanical watches are favored by the military and explorers over their quartz counterparts and have been a part of their equipment since the wristwatch was invented over 100 years ago. So the takeaway is yes a mechanical watch is up to the task but like any other piece of gear there are limits and the more you put it through the shorter the intervals between services.