You'll save time and frustration; and possibly a botched job, if you make the parts and inlet them now, saving engraving for later.
Inletting a part into a finished gun will almost certainly require refinishing in the area of the inlet; unless you can do that without any blemishes at all around the part. Refinishing may, or easily may not, match the rest of the gun. If it doesn't you've got mismatched finishes on both sides of the buttstock. Then folks on the forum will be responding as to the best way to fix that.
Building a Longrifle that looks, handles, and shoots like it should is a matter of proper planning and execution; and one is as important as the other. With kits the planning, and most of the work, have been done for you; but there is still a proper sequence to follow for the execution of the remaining work. Every step in the sequence has it's effect on the work that follows; and following sequence ensures that everything fits the way it should, looks the way it should, and functions the way it should.
You're nearing the end of your work, so you're past most of that. But the rule applies until the end. If you inlet them later, the outcome will vary. Perhaps you will inlet them perfectly, with no blemishes at all. Or you may end up refinishing the areas around the patch box and inlay, and get a perfect match. Or you will take the entire rifle down to the white again to get an even finish.