I used to use a thumbdrive much the same way at work a while ago. But I never had it set up in such an automatic way. You should be able to use AutoCAD's command line switches (/b & /p) to load a profile and/or startup script located on the thumbdrive. I don't use custom icons, so I don't have enough experience to know this would meet those needs.
One problem with this, sometimes you don't know which drive letter windows will assign to a flash drive, this can make customizing some things a hassle. I've been using the following script to take care of this problem. Its a batch file that "mounts" the directory it is run in as drive Z:/. Run it once to mount the directory, and run it again to remove the mount.
@echo off
if "%MAPX%"=="" setx mapx 0
:trial
if "%MAPX%"=="1" goto :unmapx
goto :mapx
goto :end
:mapx
echo Mapping drive Z:/
REM Map current directory to drive Z:
subst z: "%cd%"
setx MAPX 1
goto :end
:unmapx
echo Unmapping drive Z:/
REM move to a different directory
cd c:
REM unmap current drive z:
subst z: /d
setx MAPX 0
goto :end
:end
(This is totally not a commercial, but) I recently started using dropbox, an online synced storage, to share all of my acad customization files and profiles between my work and home computers. It's been working like a charm for the past year or so. Of course this would mean leaving a copy of the files on the work computer until you uninstalled the sync program. (Which does not seem like it would fit your bill, but then again, it might.) This might work out in a longer term temp position, but probably wouldn't be worth the hassle in a short term gig.