Hi George, I always engrave first because most of the engraving is on permanently installed items such as patchbox, cheekrest inlays ect. Then when I have to deburr the engraving cuts I do not have to worry about disturbing a finish that I have spent many hours applying. However if you are going to remove all the parts to be engraved, such as the lock and side plate, it might work out ok.
Hugh Toienjes