Load up WB again & apply a skin, then launch Outlook. If the window again fails to appear, open TaskManager & see if the outlook.exe process is running. That may give a clue & might be helpful for any of the SD staff lurking. Would also help to post your system information from the 'System info' tab of WB's Configuration dialog.
I've had no problems with OL2003 being skinned by WB (only skins the titlebar & borders, anyway) and haven't seen any other mentions of conflicts, but there are several Microsoft apps that have UI display issues under certain circumstances. The app processes are there in Task Manager but no window is displayed. MSPaint was a particular problem for me for a long time - I'd launch it, nothing would appear to happen, I'd launch it again, nothing would happen, I'd launch it a third time & maybe the window would open. I'd do whatever I wanted to do in Paint (edit a skin image usually), close Paint & then discover 3 instances of mspaint.exe still running in Task Manager. First time I thought to look in TM after repeatedly trying to launch Paint without a window opening there must have been a dozen instances of mspaint.exe running. Never could isolate the cause or find any information about it online, except that the same thing had happened to lots of other people, too. The only solution was getting a new computer (not for that reason, of course).
There was a problem with msconfig.exe's window not appearing due to a conflict with IconPackager's Repair Shell Icons function discussed in this thread. If you have IP running, might be worth limiting shell icon repair to specific apps (not including OL2003) just to see. There is an 'exclusion' function in the Repair Shell Icon dialog, which would be simpler, but it does not appear to work.
I was curious about Active Sync because I recently had to 'upgrade' to OL2003 on 2 machines in order to sync contacts with my iPhone & MobileMe (hate the OL UI, but what can you do). I still have a Tungsten PDA for one specific purpose which requires Active Sync but I only have AS on one of the two. Turns out Active Sync can cause OL2003 to remain running in memory after you've closed it and that began to happen on the machine with Active Sync immediately after I 'upgraded'. It appears to be a problem if Active Sync is installed, whether running or not, at least on my rig. The other computer has never had Active Sync installed and I've had no problems with 'missing UI' issues or failure of OL2003 or any other process to end when the Window was closed. The information I found indicated that there are other apps that may conflict and other reasons within OL's own settings for the failure of the process to terminate, particularly if you have it set to empty the Deleted Items folder on close. Haven't seen anything on failure of the window to appear on launch, though.
In case there are other folks having problems with OL's process not ending when the app is closed, there is a nifty little System Tray utility that will let you kill it with 2 clicks - KnockOut.