Unlikely, Casio watches not dated as such. On back of watch should be two numbers a model number (e.g. F-91W, DW-6500) then a Module Number a 3 or 4 digit number in a rectangular box.
Might be possible to give an idea of age from when models were introduced / finished. Depending on Model an average Casio Watch battery can last 2 to 10 years! Lower end for the silver oxide batteries (more "dumpy", with a variety of model numbers) and higher end for Lithium cells (size of a 5p or 10p with a 4 digit number - with a preface of letters - where first two numbers are diameter in MM and second thickness in tenths of a mm).
Was in marked with a "WR" or Water Resistant indicator? if 50M or above it should have lasted, if just WR then that indicates a "30M" water resistance - which sounds good but in reality is occasional splashes! not submersion of any type.
KevinR