Hi Steven,
I see no problem at all working in one document.
Provided the ICC output profile is the same for all pages.
If not, because the printers are doing the cover with e.g. coated and all inside pages with uncoated stock, you are facing some hurdles if doing all within one document. Not a real problem, but you have to be aware that you should do use different output settings for cover and inner pages.
However, if you want to present the customer one single PDF/X file where two different kinds of paper stock should be simulated or colors color managed differently, then you can tell the customer: No, that's not possible. Yet, PDF is not at the point that different output intents are supported with one PDF file, but that will change with PDF 2.0 soon. Let's see when InDesign will support this.
Back to working in one document with all 20 pages.
Example with facing pages for the cover:
( Maybe it's to your personal convenience to work on facing pages with cover pages where cover page 4 is left to cover page 1. )
4 Sections in the document:
Section 1 is the back cover ( also named cover page 4 ),
section 2 is cover plus cover page 2
section 3 is cover page 3
20,1 is the outer cover.
2,19 is the inner cover.
Section 4 starts the range of pages for the inner pages beginning with page 3:

Output for cover would be:
EDIT: 20,1,2,19 1,2,19,20 where possibly 20,1 and 2,19 could be exported as spreads.
Output for inside pages would be:
3-18
Output for client—if the client does not want to see backcover and cover in one spread:
1,2,3-18,19,20
Without facing pages for the cover:
Simply have a 20 page document starting with page 1 right from the spine and ending with page 20 left from the spine.
Output page numbers would be the same from above.
Starting inside pages with page number 1:
Add a new section on page 3 beginning counting with 1 and ending on page 18.
Start a new section on page 19 that will be cover page 3.
Perhaps use a different naming scheme for the cover:
C1, C2, C3, C4.
When exporting to PDF best use absolute page numbers for the cover pages:
Output for cover would be:
+1,+2,+19,+20
Output for inside pages could be:
+3-+18
Or:
1-18
Output for client:
All
Regards,
Uwe