Until recently, not very easily. You can access DOS 6.X volumes from the DOS emulator ("What software does Linux support? "), but it's harder than accessing a normal DOS volume via the DOS kernel option, a module, or mtools.
There is a recently added package, dmsdos, that reads and writes compressed file systems like DoubleSpace/DriveSpace in MS-DOS 6.x and Win95, as well as Stacker versions 3 and 4. It is a loadable kernel module. Look at ftp://metalab.unc.edu/pub/Linux/system/filesystems/dosfs/.