It might be possible to do with softlinks in the host filesystem?
It is ... Not advisable, as it requires creating a "Strange Loop" with regard to the filesystem, but say for instance:
Host: Linux
/home/Someuser/Dosbox/C
This is the path to the C drive.
Inside the ./C folder, there is a symbolic link, linking to /home/Someuser/Dosbox
eg,
ln -s /home/Someuser/Dosbox/C/Dosbox /home/Someuser/Dosbox
Dosbox will treat the symbolic link like a folder, even though it points above the root. This kind of thing is a "Strange Loop"
It is "Not Advisable", because you can have an infinitely recursed path:
C:\Dosbox\C\Dosbox\C\Dosbox\C........
Any kind of program that tries to parse a tree structure, (Like TREE.EXE from DOS) will have a VERY bad day.
Host: Windows
The VERY SAME THING can be done with NTFS using the FSUTIL command to create a hardlink, which will do THE VERY SAME THING... (only caveat, is that a hardlink has to be within the same physical volume, where a linux softlink can POINT ANYWHERE AT ALL)
Microsoft command reference for the needed fsutil invocation
The EXACT SAME PROBLEM with strange loops applies, and is, AGAIN, NOT RECOMMENDED.
This does not PREVENT Dosbox from doing anything, mind-- it just allows you to see above where your C drive was mounted. (By abusing fancy features of the filesystem to do it, and confusing the shit out of both people and software that tries to walk the directory tree.)