Not a good idea mdengraver, especially if you are going to have the piece case hardened. There is no quick way to inlay except maybe damascene, but it sounds good if you could use solder. If you aren't goint to heat treat the metal after engraving you could probably get away without messing up the piece.......watch out!! That is risky business and you need to know what you are doing.
You could do this with jewelry making techniques on other items...........Ron S
Sometimes in the shop when we were making personal tools we would stamp our names with letter stamps and flux that area and cover it with brazing alloy, then file the puddle flat, leaving the letters filled with braze. These parts weren't heat treated, though. As Ron said I think you would have a lot of trouble with parts that had been heat treated or need to be blued. Also, there is a precious metal clay type product that is a 22k gold paint. You can apply several coats to fill in details on silver jewelry, and fire it and it will produce a shiny 22k gold inlay. Don't know if it will stick to other metals, though. I want to do a sterling signet ring with a gold inlay and I considered this but I think I am just going to inlay 24k sheet.