I read (
saw) a technique for doing this stuff (wood inlays) that is something I need to try someday.
With complex inlay, you do as you say, lase the pattern into your base wood with the appropriate kerf.
Then you place your inlay wood onto a strip of aluminum ducting tape.
With your inlay pattern (flipped since the face side is against the tape), you lase the pattern. Burn away to depth all the negative space. Don't know about a CO2, but a diode laser will not cut through the tape. You don't really need to go full depth (through cut on the inlay wood), just enough to get a thickness appropriate for your base wood etch.
Now you just smear glue into your base wood etch, align the taped inlay so it drops into the base wood and press (hammer) the taped inlay home.
Not really needed for simple inlays, but with intricate patterns this avoids the tedium of placing delicate bits by hand and if the pattern is very fragile it can avoid the expected disasters.