Not sure about the depth. I have had them drop down inside the jacket, however. They always have been able to be retrieved. Pull it up and grab it with a big pair of vice-grips, and pry it out.
Get a spare freeze plug before you start, just in case the heater is too long.
Also, if you can take your tractor by a radiator shop after the plug is installed they can pressure test the system. They will fill it with water and pump air in to pressurre it up to about 16 PSI. Any leak becomes apparent.
Jim