How is that different to
You wear your watch while welding and grinding and you gouge the case and bezel and then expect Omega to cover replacement parts?
The main difference is that movement parts such as gears and springs are normal wear and tear and replaced without additional cost as part of the Omega service. Destroying the case and bezel are additional costs and the service replacements may be different than the originals. Most people still consider a watch original condition even if something like a main spring has been replaced, whereas a new case, bezel, dial, hands is not considered original. While it is good to play devil's advocate to come up with a solution, abusing a watch by welding or putting it in a wood chipper is not the same scenario.
But OP should recognize that the lubricants have dried and hardened and running the watch will wear out the movement parts, as said by other members.
Another factor is how often the watch will be worn. If a daily, then it needs to be serviced now. If in rotation with a dozen or so watches, then it receives less wear.
Also, if the movement is old and replacement parts are not available, then immediately service. But if replacement parts are readily available and the watch isn't worn often, then consider delaying servivce. That's playing devil's advocate, imho, not wearing your watch while welding.
BTW, I used to weld in a factory that made skid steer loaders ( like Bobcats, but not a Bobcat) and also in a factory that made horse trailers. I had belt buckles with welding splatter. But I wore leather gloves and arm protectors so never got my watch splattered or received grinding marks. I think a welder who gets grinding marks on their watch will have more serious problems than just destroying their watch.