In the B737MRG there is comment on technique to manage a dual FMC failure airborne. It is mentioned that map mode can still be used and suggests selecting STA and WPT in order to navigate to positions using heading select.
If both fmc fail,the use of LNAV is not possible so you need to navigate using conventional navigation such as VOR radials/ndbs..if your departure or arrival allows,in flight if both fmcs do remain failed,open the enroute charts and start using those vor...you can always ask for vectors if 1 you trust the ATC and 2 you have no other choice.
Now if you fly a departure with no raw data info(vor,ndb) then if IMC make sure you climb above the MSA and go from there.
As for the technical part of your question,when both fmcs failed in the sim,the MAP flag was on and all the navigation screen was dark.
There is no info in QRh on using heading to navigate on a 'failed' map and i would caution any not to do that even if your book suggests some backround data may still be displayed.
If you manage a dual fmc using hdg sel on a failed fmc map,i doubt you'll pass your check...just saying
,last resort in a total loss of situational awareness i would say....