I would say it would not cause a problem. If you have the 4 wheels on the car and add the spare after, you should be ok. The system on a 04 will learn and keep the memory of each wheel and its position by the id of the sensor. If you simply rotate the tires, the system should be reset and driven till the sensors learn again what wheel is where. The stationary one in the trunk should not be picked up as one of the wheel mounted.
This is correct, the system learns the ID of each wheel sensor but you don't explain how the system does this and does not get confused with the message from the spare.
The 2004 system appears to use statistical signal strength measurements from each sensor, now that it has an antenna close to each wheel, the TPMS messages from the spare are received weaker than those from the mounted wheels. I did not find a good WIS reference but the component supplier explains this (see 4.5.1):
My W211 had this Beru system but the car did not have a spare tyre and I never experienced this in practise (we use winter tyres and an unused summer/winter tyre could have been used as a spare but the W211 trunk does not have room for a spare if it came without one from the factory).
The later Siemens system cannot use this method as it does not have a sensor antenna for each wheel. GF4015P5126SX however clearly explains that the car would (automatically) detect a mounted spare wheel within a few minutes. I did not find a technical explanation but this must be based on the fact that the sensor transmits wheel acceleration info within each tyre pressure message, the system can then identify mounted wheels in motion from the spare.