I am a programmer, or at least was a few years ago. Just new to the Mac world.
No, the Hazel menubar icon is not visible after logging in. Hence the helper app not showing up in Activity Monitor.
In fact, I just saw something even more interesting. When I went to add TextEdit to the Login Items list, I noticed that HazelHelper wasn't in the list. So I switched to the Hazel Preference Pane, then back to the Accounts Preference pane and low and behold, HazelHelper is now in the list.
What I tried to say before was that until Hazel's preference pane is displayed, Hazel doesn't seem to be running. As soon as I open the preference pane, it's menubar item appears and the helper app appears in Activity Monitor.
I looked at the console logs. The only error I see after logging out and back in is a program called MenuCracker that tells me to ignore the next error message. MenuCracker is used by iStat Menus and GeekTool and others on my system so I do expect that.
iStat Menu's seems to launch fine and so does TextExpander now.
Hopefully, the above new info will be of some help. I haven't seen items in the Login Items appear and disappear like that before. This is really looking more and more like a bug in Leopard.