I have seen this done. Or rather, I have seen the resulting part. Haven't tried it myself.
The secret is to make the insert so that it drops completely into the part you already have printed. That is, the insert has to be flush with the top of the print at the time you drop it in, or slightly below that. That way the printhead won't run into anything. This may mean bedding the insert in a thin layer of adhesive that can be squeezed out when you push the insert in.
It also means that the top of the insert needs to be flat. 3D printers don't do a good job of printing on air.
Also, while most modern printers can be paused, they will only move the printhead off to the side a bit. You won't have much room in there to work. If your printer is enclosed, and you will need that enclosure to make good prints in ABS, you have only the front opening to reach in and insert something. This could be tricky.
One warning about printers that are "self-leveling" -- they aren't. What they really do is measure the off-level bed and then compensate for that by laying down more filament in the low spots. This means the bottom won't be parallel to the top of the print. This may or may not matter to you. My opinion is that a carefully leveled bed is essential to getting a good print.