A recovery Magnet will probably not pick up a Rolex due to its non-magnetic stainless steel alloy. To verify my memory that some stainless is non-magnetic I did the following searches:
From a Google search: Stainless steels are iron-based alloys primarily known for their generally excellent corrosion resistance, which is largely due to the steel's chromium concentration. There are several different types of stainless steels. The two main types are austenitic and ferritic, each of which exhibits a different atomic arrangement. Due to this difference, ferritic stainless steels are generally magnetic while austenitic stainless steels usually are not.
From Rolex's site: Rolex uses 904L stainless steel which is commonly used in high-technology and in the aerospace and chemical industries. Its excellent anti-corrosion properties, comparable to those of precious metals, are due to its high chrome content.
From a Google search: 904L is an Austenitic Nonstandard grade Stainless Steel. It is composed of (in weight percentage) 0.02% Carbon (C), 2.00% Manganese (Mn), 1.00% Silicon (Si), 19.0-23.0% Chromium (Cr), 23.0-28.0% Nickel (Ni), 0.045% Phosphorus (P), 0.035% Sulfur (S), 4.0-5.0% Molybdenum (Mo), 1.0-2.0% Copper (Cu), and the base metal Iron (Fe). Other designations of 904L stainless steel include UNS N08904 and ASTM B625.