If you have your drives mapped with drive letters you can run the following script (say daily) to have it generate a file list per drive and place in DropBox:
for %%i in (C D E F G H I J K L M N O P Q R S T U V W X Y Z) DO (
if exist %%i: (
dir %%i:\ /ahs /s /b > "%dropbox%\FileList_%%i.txt" 2> nul
If you don't want to assign driveletters you can also mount all your disks under a single mount point instead of drive letters (say C:\PoolDisks\) and just dir that folder.