Taking a cheap Timex off your wrist and putting it in a locker would certainly not be a problem, and you could certainly do it.
The POINT of owning an Omega, however, is that they are fairly distinctive watches that are very cool AND expensive looking, and if you know anything at all about Omegas, you know that they cost a LOT more than a thousand bucks. (Obviously a gold Omega will scream "steal me!!" a lot louder than the SS version. The Ti versions are relatively "stealthy", and that gunmetal gray color doesn't attract very much attention in ANY setting.) Taking off a four figure watch in front of a bunch of strangers is simply NOT a good strategic move on your part. Leaving it behind in a locker protected by a cheap $5 lock that anybody could break in 5 seconds flat is even an worse move. If you're an old fart like me, you can add memory problems (did I put the watch in the locker, and did I remember to lock the locker???) on top of that.
Buy an Omega with a 300 meter depth rating, and leave the sucker on your wrist, regardless of what you're doing or where you are. If you're a watchaholic, you can rationalize a sport watch, beater watch, and dress watch (all of them Omegas...) if you want to. In ANY case, however, it's simpler to buy a watch that fits 100% into your life, rather than having to change your life a few percent to accomodate some of the limitations of your watch.