Don’t mind the squirell, he just likes to crack nuts!!
For my opinion .... not on this case to me but yes, some engravings can add a sentimental or historic value.
Military engravings often add value. Significant dates or names or text add value if you can prove they where somehow related to the watch. I.E. an astronaut engraving the watch after wearing it on the moon.... or before.... or during ( that would be something). A Daytona being worn at Daytona or awarded at Daytona..... a submariner with Jacques Cousteau’s initials.... some mike tRy guys unit...
There are collectors that actually look for engraved watches because they like the story behind their watches.... other hate them.
You do you!!