I asked the same question a while ago. The general consensus was there is no need to hide them.
But a dealer I have purchased several watches from who has a healthy business in high end watches told me that for expensive watches, replica companies are constantly searching the internet for serial numbers and that some high end watch companies (for example Audemars Piguet) have databases of "compromised" serial numbers and you can call them with a serial number and they will check it for you. But from what this dealer said, unless your watch is rather pricey ($30,000 and up), I don't think you need to t worry about hiding serial numbers.
A forum community dedicated to watch owners and enthusiasts. Come join the discussion about watch collections, displays, watch winders, accessories, classifieds, and more! We welcome all manufacturers including Casio G-Shock, OMEGA, Rolex, Breitling, Rolex and Tudor, Seiko, Grand Seiko and others.