To answer my own question: it works!
The procedure I used:
1. remove power cable from Falcon and take the Falcon case apart until the mainboard is accessible
2. remove jumper from BS1 (to be able to put TOS4DFB1 in Bank 1 if you want to keep the original TOS 4.04 in Bank 0)
3. put jumper on DISABLE
4. reinstall original Falcon ROM chip (requires removal of the RAM board
5. reconnect power cable and power on system; it should now come up with the standard TOS 4.04 and no LEDs should be lit on the DFB1X
6. run DFBFLASH.TTP (from FLASH UTIL (FIXED) on
https://exxosforum.co.uk/atari/last/DFB1X/) and enter TOS4DFB1.IMG (or drag the IMG file on the TTP
7. when asked if the Flash should be erased I choose "N", since it mentioned that erasing would actually erase everything
8. wait for writing and verifying to be successfully finished
9. power down system
10. remove jumper from DISABLE and also remove the original ROM chip again
11. power on system; at the memory test it now tests both the standard RAM and the ALT RAM
12. make sure that MAPROM_C.PRG is not enabled in the AUTO folder
13. after verifying everything works as expected reassemble the Falcon case